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Incubator escapee wiki:WikiProject Mathematics/PlanetMath Exchange/53-XX Differential geometry
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__NOTOC__ {{Planetmath instructions|topic=53-XX Differential geometry}} ==53-00 General reference works (handbooks, dictionaries, bibliographies, etc.)== * PM: [http://planetmath.org/?op=getobj&from=objects&id=4146 closed differential forms on a simply connected domain], id=4146 -- WP guess: [[closed differential forms on a simply connected domain]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6541 distribution], id=6541 -- WP guess: [[distribution (differential geometry)]] -- Status: '''C''' ::[[User:Jtwdog|Jtwdog]] 21:16, 21 October 2005 (UTC) <br/> ::Filled it in ...briefly [[User:Robbjedi|Robbjedi]] 03:19, 23 October 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3669 exact (differential form)], id=3669 -- WP: [[exact (differential form)]] -- Status: '''A''' ::[[User:Jtwdog|Jtwdog]] 21:16, 21 October 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6441 fundamental concepts in differential geometry], id=6441 -- WP guess: [[fundamental concepts in differential geometry]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5512 integral curve], id=5512 -- WP: [[integral curve]] -- Status: '''A''' ::[[User:Jtwdog|Jtwdog]] 21:16, 21 October 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=5591 Lie bracket], id=5591 -- WP: [[Lie derivative]] -- Status: '''A''' ::[[User:Linas|linas]] 04:40, 11 Apr 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3707 Lie derivative], id=3707 -- WP: [[Lie derivative]] -- Status: '''A''' ::[[User:Linas|linas]] 04:38, 11 Apr 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=5590 Lie derivative (for vector fields)], id=5590 -- WP: [[Lie derivative]] -- Status: '''A''' ::[[User:Linas|linas]] 04:38, 11 Apr 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=5692 locally Euclidean], id=5692 -- WP: [[manifold|locally Euclidean]] -- Status: '''A''' ::[[User:Jtwdog|Jtwdog]] 21:16, 21 October 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=1981 manifold], id=1981 -- WP: [[manifold]] -- Status: '''A''' ::[[User:Jtwdog|Jtwdog]] 21:16, 21 October 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=5611 manifold], id=5611 -- WP: [[manifold]] -- Status: '''A''' ::[[User:Jtwdog|Jtwdog]] 21:16, 21 October 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=4364 metric tensor], id=4364 -- WP: [[metric tensor]] -- Status: '''A''' ::[[User:Linas|linas]] 04:43, 11 Apr 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=5691 notes on the classical definition of a manifold], id=5691 -- WP guess: [[notes on the classical definition of a manifold]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5509 Poincaré lemma], id=5509 -- WP: [[Poincaré lemma]] -- Status: '''NM''' ::[[User:Linas|linas]] 19:41, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=4147 proof of closed differential forms on a simple connected domain], id=4147 -- WP guess: [[proof of closed differential forms on a simple connected domain]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5912 proof of Poincaré lemma], id=5912 -- WP guess: [[proof of Poincaré lemma]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4895 pullback of a k-form], id=4895 -- WP guess: [[pullback of a k-form]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5506 tangent map], id=5506 -- WP guess: [[tangent map]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=2007 tangent space], id=2007 -- WP guess: [[tangent space]] -- Status: '''A''' ::[[User:Jtwdog|Jtwdog]] 21:16, 21 October 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=5693 topological manifold], id=5693 -- WP: [[topological manifold]] -- Status: '''A''' ::[[User:Linas|linas]] 04:45, 11 Apr 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=5731 bibliography for differential geometry], id=5731 -- WP guess: [[bibliography for differential geometry]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7205 commuting vector fields], id=7205 -- WP guess: [[commuting vector fields]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7103 exhaustion by compact sets], id=7103 -- WP guess: [[exhaustion by compact sets]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7063 integral curve], id=7063 -- WP guess: [[integral curve]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7472 proof of d\alpha (X,Y) = X(\alpha(Y)) - Y(\alpha(X)) - \alpha([X,Y]) (global coordinate-free)], id=7472 -- WP: [[Lie derivative]] -- Status: '''N''' ::PM article is confusingly written. [[User:Linas|linas]] 19:46, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7471 proof of d\alpha (X,Y) = X(\alpha(Y)) - Y(\alpha(X)) - \alpha([X,Y]) (local coordinates)], id=7471 -- WP: [[Lie derivative]] -- Status: '''N''' ::PM article is confusingly written. [[User:Linas|linas]] 19:46, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7335 submersion], id=7335 -- WP: [[submersion]] -- Status: '''A''' ::[[User:Linas|linas]] 19:51, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7850 proof of exhaustion by compact sets for \mathbb{R}^n], id=7850<sup><span style="color:red;">new!</span></sup> -- WP guess: [[proof of exhaustion by compact sets for \mathbbR^n]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8081 topological manifold], id=8081<sup><span style="color:red;">new!</span></sup> -- WP guess: [[topological manifold]] -- Status: ==53-01 Instructional exposition (textbooks, tutorial papers, etc.)== * PM: [http://planetmath.org/?op=getobj&from=objects&id=3110 curl], id=3110 -- WP: [[Curl (mathematics)|curl]] -- Status: '''A''' ::[[User:Jtwdog|Jtwdog]] 21:19, 21 October 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7341 alternate characterization of curl], id=7341 -- WP guess: [[alternate characterization of curl]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7681 Christoffel symbols], id=7681<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Christoffel symbols]] -- Status: ==53-03 Historical (must also be assigned at least one classification number from Section 01)== ==53A04 Curves in Euclidean space== * PM: [http://planetmath.org/?op=getobj&from=objects&id=1632 curvature (space curve)], id=1632 -- WP guess: [[curvature (space curve)]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=1660 Frenet frame], id=1660 -- WP guess: [[Frenet frame]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=3929 fundamental theorem of space curves], id=3929 -- WP guess: [[fundamental theorem of space curves]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=3928 helix], id=3928 -- WP guess: [[helix]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=1636 Serret-Frenet equations], id=1636 -- WP guess: [[Serret-Frenet equations]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=1633 space curve], id=1633 -- WP guess: [[space curve]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7074 Classical differential geometry], id=7074 -- WP guess: [[Classical differential geometry]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7393 curvature (plane curve)], id=7393 -- WP guess: [[curvature (plane curve)]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7100 cycloid], id=7100 -- WP guess: [[cycloid]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7390 DNA Inequality], id=7390 -- WP guess: [[DNA Inequality]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7102 ellipse], id=7102 -- WP guess: [[ellipse]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7624 example of curvature (space curve)], id=7624 -- WP guess: [[example of curvature (space curve)]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7567 expressions for curvature and torsion], id=7567 -- WP guess: [[expressions for curvature and torsion]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7073 famous curves], id=7073 -- WP guess: [[famous curves]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7108 line in the plane], id=7108 -- WP guess: [[line in the plane]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7392 Mean Curvature], id=7392 -- WP guess: [[Mean Curvature]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7072 Serret-Frenet equations in \mathbb{R}^2], id=7072 -- WP guess: [[Serret-Frenet equations in \mathbbR^2]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7101 sinusoid], id=7101 -- WP guess: [[sinusoid]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9277 circle of curvature], id=9277<sup><span style="color:red;">new!</span></sup> -- WP guess: [[circle of curvature]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9353 curvature determines the curve], id=9353<sup><span style="color:red;">new!</span></sup> -- WP guess: [[curvature determines the curve]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7820 curvature of a circle], id=7820<sup><span style="color:red;">new!</span></sup> -- WP guess: [[curvature of a circle]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9350 curvature of Nielsen's spiral], id=9350<sup><span style="color:red;">new!</span></sup> -- WP guess: [[curvature of Nielsen's spiral]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7689 easy calculation of the area of an ellipse], id=7689<sup><span style="color:red;">new!</span></sup> -- WP guess: [[easy calculation of the area of an ellipse]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8606 moving frame], id=8606<sup><span style="color:red;">new!</span></sup> -- WP guess: [[moving frame]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9278 order of contact], id=9278<sup><span style="color:red;">new!</span></sup> -- WP guess: [[order of contact]] -- Status: ==53A05 Surfaces in Euclidean space== * PM: [http://planetmath.org/?op=getobj&from=objects&id=7321 Pappus's centroid theorem], id=7321 -- WP guess: [[Pappus's centroid theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7339 second fundamental form], id=7339 -- WP: [[second fundamental form]] -- Status: '''NM''' ::[[User:Linas|linas]] 19:55, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=8807 Gauss-Bonnet theorem], id=8807<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Gauss-Bonnet theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8824 Gauss-Bonnet theorem], id=8824<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Gauss-Bonnet theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9299 Gaussian curvature], id=9299<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Gaussian curvature]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8132 shape operator], id=8132<sup><span style="color:red;">new!</span></sup> -- WP guess: [[shape operator]] -- Status: ==53A17 Kinematics== ==53A30 Conformal differential geometry== ==53A35 Non-Euclidean differential geometry== * PM: [http://planetmath.org/?op=getobj&from=objects&id=5769 Smarandache geometries], id=5769 -- WP: [[Smarandache geometries]] -- Status: '''N''' ::PM article is "not found", this PM link is broken? [[User:Linas|linas]] 19:37, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7327 Smarandache geometries], id=7327 -- WP: [[Smarandache geometries]] -- Status: '''NC''' ::Current WP link is redirect to biography of Smarandache. 19:37, 5 March 2006 (UTC) ==53A45 Vector and tensor analysis== * PM: [http://planetmath.org/?op=getobj&from=objects&id=3668 closed (differential form)], id=3668 -- WP: [[closed (differential form)]] -- Status: '''A''' ::[[User:Jtwdog|Jtwdog]] 21:21, 21 October 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7031 axial vector], id=7031 -- WP: [[axial vector]] -- Status: '''A''' ::[[User:Linas|linas]] 19:09, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=9611 circulation and vorticity], id=9611<sup><span style="color:red;">new!</span></sup> -- WP guess: [[circulation and vorticity]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7944 continuity equation], id=7944<sup><span style="color:red;">new!</span></sup> -- WP guess: [[continuity equation]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9376 derivation of the Laplacian from rectangular to spherical coordinates], id=9376<sup><span style="color:red;">new!</span></sup> -- WP guess: [[derivation of the Laplacian from rectangular to spherical coordinates]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9321 derivation of unit vectors in curvilinear coordinates], id=9321<sup><span style="color:red;">new!</span></sup> -- WP guess: [[derivation of unit vectors in curvilinear coordinates]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7889 motion of continuum], id=7889<sup><span style="color:red;">new!</span></sup> -- WP guess: [[motion of continuum]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8048 Reynolds transport theorem], id=8048<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Reynolds transport theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7911 time dilatation of a volume element], id=7911<sup><span style="color:red;">new!</span></sup> -- WP guess: [[time dilatation of a volume element]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7804 topics on vectors], id=7804<sup><span style="color:red;">new!</span></sup> -- WP guess: [[topics on vectors]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7863 vector fields: Lagrangian and Eulerian description], id=7863<sup><span style="color:red;">new!</span></sup> -- WP guess: [[vector fields: Lagrangian and Eulerian description]] -- Status: ==53A55 Differential invariants (local theory), geometric objects== * PM: [http://planetmath.org/?op=getobj&from=objects&id=8592 Riemann curvature tensor], id=8592<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Riemann curvature tensor]] -- Status: ==53A99 Miscellaneous== * PM: [http://planetmath.org/?op=getobj&from=objects&id=1318 Euclidean distance], id=1318 -- WP guess: [[Euclidean distance]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5419 some structures on \mathbb{R}^n], id=5419 -- WP guess: [[some structures on \mathbbR^n]] -- Status: ==53Axx Classical differential geometry== ==53B05 Linear and affine connections== * PM: [http://planetmath.org/?op=getobj&from=objects&id=6191 affine connection], id=6191 -- WP: [[affine connection]] -- Status: '''NM''' ::[[User:Linas|linas]] 04:23, 11 Apr 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6159 conjugate points], id=6159 -- WP guess: [[conjugate points]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=2880 connection], id=2880 -- WP: [[connection]] -- Status: '''NM''' ::The PM article is quite a bit larger [[User:Linas|linas]] 04:25, 11 Apr 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=4765 Levi-Civita connection], id=4765 -- WP: [[Levi-Civita connection]] -- Status: '''A''' ::[[User:Linas|linas]] 04:29, 11 Apr 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6157 Riemann normal coordinates], id=6157 -- WP guess: [[Riemann normal coordinates]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4755 vector field along a curve], id=4755 -- WP guess: [[vector field along a curve]] -- Status: ==53B20 Local Riemannian geometry== * PM: [http://planetmath.org/?op=getobj&from=objects&id=7355 Euclidean space as a manifold], id=7355 -- WP guess: [[Euclidean space as a manifold]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7332 first fundamental form], id=7332 -- WP guess: [[first fundamental form]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7325 first order operators in Riemannian geometry], id=7325 -- WP guess: [[first order operators in Riemannian geometry]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7446 formulas in Riemannian geometry], id=7446 -- WP guess: [[formulas in Riemannian geometry]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7907 sectional curvature], id=7907<sup><span style="color:red;">new!</span></sup> -- WP guess: [[sectional curvature]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7924 sectional curvature determines Riemann curvature tensor], id=7924<sup><span style="color:red;">new!</span></sup> -- WP guess: [[sectional curvature determines Riemann curvature tensor]] -- Status: ==53B21 Methods of Riemannian geometry== * PM: [http://planetmath.org/?op=getobj&from=objects&id=4120 Hodge star operator], id=4120 -- WP: [[Hodge star operator]] -- Status: '''NM''' * PM: [http://planetmath.org/?op=getobj&from=objects&id=3452 Riemannian manifold], id=3452 -- WP: [[Riemannian manifold]] -- Status: '''NM''' ==53B25 Local submanifolds== ==53B99 Miscellaneous== * PM: [http://planetmath.org/?op=getobj&from=objects&id=6235 example of rewriting a differential equation as a Pfaffian system], id=6235 -- WP guess: [[example of rewriting a differential equation as a Pfaffian system]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=3501 germ of smooth functions], id=3501 -- WP guess: [[germ of smooth functions]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6210 Pfaff's problem], id=6210 -- WP guess: [[Pfaff's problem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9801 germ], id=9801<sup><span style="color:red;">new!</span></sup> -- WP guess: [[germ]] -- Status: ==53Bxx Local differential geometry== ==53C17 Sub-Riemannian geometry== * PM: [http://planetmath.org/?op=getobj&from=objects&id=4754 Sub-Riemannian manifold], id=4754 -- WP: [[Sub-Riemannian manifold]] -- Status: '''A''' ::[[User:Linas|linas]] 04:48, 11 Apr 2005 (UTC) ==53C20 Global Riemannian geometry, including pinching== * PM: [http://planetmath.org/?op=getobj&from=objects&id=7905 sphere theorem from global differential geometry], id=7905<sup><span style="color:red;">new!</span></sup> -- WP guess: [[sphere theorem from global differential geometry]] -- Status: ==53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions== ==53C22 Geodesics== * PM: [http://planetmath.org/?op=getobj&from=objects&id=6164 affine parameter], id=6164 -- WP guess: [[affine parameter]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5513 geodesic], id=5513 -- WP: [[geodesic]] -- Status: '''A''' ::[[User:Linas|linas]] 04:33, 11 Apr 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=9510 geodesic triangle], id=9510<sup><span style="color:red;">new!</span></sup> -- WP guess: [[geodesic triangle]] -- Status: ==53C26 Hyper-Kähler and quaternionic Kähler geometry, ''special'' geometry== * PM: [http://planetmath.org/?op=getobj&from=objects&id=7813 hyperkähler manifold], id=7813<sup><span style="color:red;">new!</span></sup> -- WP guess: [[hyperkähler manifold]] -- Status: ==53C40 Global submanifolds== ==53C42 Immersions (minimal, prescribed curvature, tight, etc.)== * PM: [http://planetmath.org/?op=getobj&from=objects&id=7569 Nash isometric embedding theorem], id=7569 -- WP: [[Nash isometric embedding theorem]] -- Status: '''NC''' ::[[User:Linas|linas]] 20:06, 5 March 2006 (UTC) ==53C60 Finsler spaces and generalizations (areal metrics)== * PM: [http://planetmath.org/?op=getobj&from=objects&id=7372 spray space], id=7372 -- WP: [[spray space]] -- Status: '''NC''' ::[[User:Linas|linas]] 20:05, 5 March 2006 (UTC) ==53Cxx Global differential geometry== ==53D05 Symplectic manifolds, general== * PM: [http://planetmath.org/?op=getobj&from=objects&id=3739 almost complex structure], id=3739 -- WP: [[almost complex structure]] -- Status: '''A''' ::[[User:Linas|linas]] 17:45, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=4760 coadjoint orbit], id=4760 -- WP: [[coadjoint orbit]] -- Status: '''NM''' ::[[User:Linas|linas]] 17:49, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3738 Darboux's Theorem (symplectic geometry)], id=3738 -- WP: [[Darboux's theorem]] -- Status: '''A''' ::[[User:Linas|linas]] 18:15, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3672 examples of symplectic manifolds], id=3672 -- WP: [[symplectic manifold]] -- Status: '''NM''' ::[[User:Linas|linas]] 18:19, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6410 Hamilton equations], id=6410 -- WP: [[Hamilton's equations]] -- Status: '''NM''' ::[[User:Linas|linas]] 18:29, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3706 Hamiltonian vector field], id=3706 -- WP: [[Hamiltonian vector field]] -- Status: '''A''' ::[[User:Jtwdog|Jtwdog]] 21:37, 21 October 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6422 if the algebra of functions on a manifold is a Poisson ring then the manifold is symplectic], id=6422 -- WP: [[Poisson ring]] -- Status: '''N''' ::Its a proof, can be replaced by a sentance and a ref in WP. [[User:Linas|linas]] 17:09, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3670 isotropic submanifold], id=3670 -- WP: [[isotropic submanifold]] -- Status: '''NC''' ::current WP article is a redirect. [[User:Linas|linas]] 18:33, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3671 lagrangian submanifold], id=3671 -- WP: [[lagrangian submanifold]] -- Status: '''A''' ::PM article is a stub, WP article is redirect.[[User:Linas|linas]] 18:36, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3806 Moser's theorem], id=3806 -- WP: [[Moser's theorem]] -- Status: '''NC''' ::[[User:Linas|linas]] 18:38, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6412 Poisson bracket], id=6412 -- WP: [[Poisson bracket]] -- Status: '''A''' ::[[User:Linas|linas]] 20:03, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6414 Poisson ring], id=6414 -- WP: [[Poisson ring]] -- Status: '''C''' ::[[User:Linas|linas]] 04:54, 11 Apr 2005 (UTC) ::[[User:Linas|linas]] 17:06, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=5589 proof of Darboux's Theorem (symplectic geometry)], id=5589 -- WP: [[Darboux's Theorem]] -- Status: '''N''' ::added ref to WP article. [[User:Linas|linas]] 21:07, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3667 symplectic manifold], id=3667 -- WP: [[symplectic manifold]] -- Status: '''NM''' ::This should be a trival merge, just pick up def for symplectomorphism, and defn of non-degeneracy. [[User:Linas|linas]] 04:53, 11 Apr 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=4140 symplectic matrix], id=4140 -- WP: [[symplectic matrix]] -- Status: '''A''' ::[[User:Linas|linas]] 04:53, 11 Apr 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3705 symplectic vector field], id=3705 -- WP: [[symplectic vector field]] -- Status: '''M''' ::[[User:Linas|linas]] 18:53, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=4138 symplectic vector space], id=4138 -- WP: [[symplectic vector space]] -- Status: '''A''' ::[[User:Linas|linas]] 18:55, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7099 Examples of lagrangian submanifolds], id=7099 -- WP: [[Lagrangian submanifold]] -- Status: '''NM''' ::[[User:Linas|linas]] 19:07, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7455 The characteristic polynomial of a symplectic matrix is a reciprocal polynomial], id=7455 -- WP: [[Symplectic matrix]] -- Status: '''NM''' ::Actually, [[symplectic matrix]] article just needs a statement of the theorem. [[User:Linas|linas]] 19:05, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6423 concepts in symplectic geometry], id=6423<sup><span style="color:red;">new!</span></sup> -- WP guess: [[concepts in symplectic geometry]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7685 every symplectic manifold has even dimension], id=7685<sup><span style="color:red;">new!</span></sup> -- WP guess: [[every symplectic manifold has even dimension]] -- Status: ==53D10 Contact manifolds, general== * PM: [http://planetmath.org/?op=getobj&from=objects&id=4409 contact manifold], id=4409 -- WP: [[contact manifold]] -- Status: '''NM''' ::[[User:Linas|linas]] 19:29, 5 March 2006 (UTC) ==53D20 Momentum maps; symplectic reduction== * PM: [http://planetmath.org/?op=getobj&from=objects&id=3718 momentum map], id=3718 -- WP: [[momentum map]] -- Status: '''A''' ::[[User:Linas|linas]] 19:17, 5 March 2006 (UTC) ==53D50 Geometric quantization== ==53D99 Miscellaneous== * PM: [http://planetmath.org/?op=getobj&from=objects&id=7733 \mathbb{C} as a Kähler manifold], id=7733<sup><span style="color:red;">new!</span></sup> -- WP guess: [[\mathbbC as a Kähler manifold]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8203 a Kähler manifold is symplectic], id=8203<sup><span style="color:red;">new!</span></sup> -- WP guess: [[a Kähler manifold is symplectic]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7673 Kähler manifold], id=7673<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Kähler manifold]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8740 Kähler potential], id=8740<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Kähler potential]] -- Status: ==53Dxx Symplectic geometry, contact geometry== ==53Z05 Applications to physics== * PM: [http://planetmath.org/?op=getobj&from=objects&id=8393 Minkowski space], id=8393<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Minkowski space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7688 pseudo-Riemannian manifold], id=7688<sup><span style="color:red;">new!</span></sup> -- WP guess: [[pseudo-Riemannian manifold]] -- Status:
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