Incubator escapee wiki:WikiProject Mathematics/PlanetMath Exchange/53-XX Differential geometry

53-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: closed differential forms on a simply connected domain, id=4146 -- WP guess: closed differential forms on a simply connected domain -- Status:

• PM: distribution, id=6541 -- WP guess: distribution (differential geometry) -- Status: C

Jtwdog 21:16, 21 October 2005 (UTC)

Filled it in ...briefly Robbjedi 03:19, 23 October 2005 (UTC)

• PM: exact (differential form), id=3669 -- WP: exact (differential form) -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: fundamental concepts in differential geometry, id=6441 -- WP guess: fundamental concepts in differential geometry -- Status:

• PM: integral curve, id=5512 -- WP: integral curve -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: Lie bracket, id=5591 -- WP: Lie derivative -- Status: A

linas 04:40, 11 Apr 2005 (UTC)

• PM: Lie derivative, id=3707 -- WP: Lie derivative -- Status: A

linas 04:38, 11 Apr 2005 (UTC)

• PM: Lie derivative (for vector fields), id=5590 -- WP: Lie derivative -- Status: A

linas 04:38, 11 Apr 2005 (UTC)

• PM: locally Euclidean, id=5692 -- WP: locally Euclidean -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: manifold, id=1981 -- WP: manifold -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: manifold, id=5611 -- WP: manifold -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: metric tensor, id=4364 -- WP: metric tensor -- Status: A

linas 04:43, 11 Apr 2005 (UTC)

• PM: notes on the classical definition of a manifold, id=5691 -- WP guess: notes on the classical definition of a manifold -- Status:

• PM: Poincaré lemma, id=5509 -- WP: Poincaré lemma -- Status: NM

linas 19:41, 5 March 2006 (UTC)

• PM: 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: proof of Poincaré lemma, id=5912 -- WP guess: proof of Poincaré lemma -- Status:

• PM: pullback of a k-form, id=4895 -- WP guess: pullback of a k-form -- Status:

• PM: tangent map, id=5506 -- WP guess: tangent map -- Status:

• PM: tangent space, id=2007 -- WP guess: tangent space -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: topological manifold, id=5693 -- WP: topological manifold -- Status: A

linas 04:45, 11 Apr 2005 (UTC)

• PM: bibliography for differential geometry, id=5731 -- WP guess: bibliography for differential geometry -- Status:

• PM: commuting vector fields, id=7205 -- WP guess: commuting vector fields -- Status:

• PM: exhaustion by compact sets, id=7103 -- WP guess: exhaustion by compact sets -- Status:

• PM: integral curve, id=7063 -- WP guess: integral curve -- Status:

• PM: 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. linas 19:46, 5 March 2006 (UTC)

• PM: 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. linas 19:46, 5 March 2006 (UTC)

• PM: submersion, id=7335 -- WP: submersion -- Status: A

linas 19:51, 5 March 2006 (UTC)

• PM: proof of exhaustion by compact sets for \mathbb{R}^n, id=7850^new! -- WP guess: proof of exhaustion by compact sets for \mathbbR^n -- Status:

• PM: topological manifold, id=8081^new! -- WP guess: topological manifold -- Status:

53-01 Instructional exposition (textbooks, tutorial papers, etc.)

• PM: curl, id=3110 -- WP: curl -- Status: A

Jtwdog 21:19, 21 October 2005 (UTC)

• PM: alternate characterization of curl, id=7341 -- WP guess: alternate characterization of curl -- Status:

• PM: Christoffel symbols, id=7681^new! -- WP guess: Christoffel symbols -- Status:

53A04 Curves in Euclidean space

• PM: curvature (space curve), id=1632 -- WP guess: curvature (space curve) -- Status:

• PM: Frenet frame, id=1660 -- WP guess: Frenet frame -- Status:

• PM: fundamental theorem of space curves, id=3929 -- WP guess: fundamental theorem of space curves -- Status:

• PM: helix, id=3928 -- WP guess: helix -- Status:

• PM: Serret-Frenet equations, id=1636 -- WP guess: Serret-Frenet equations -- Status:

• PM: space curve, id=1633 -- WP guess: space curve -- Status:

• PM: Classical differential geometry, id=7074 -- WP guess: Classical differential geometry -- Status:

• PM: curvature (plane curve), id=7393 -- WP guess: curvature (plane curve) -- Status:

• PM: cycloid, id=7100 -- WP guess: cycloid -- Status:

• PM: DNA Inequality, id=7390 -- WP guess: DNA Inequality -- Status:

• PM: ellipse, id=7102 -- WP guess: ellipse -- Status:

• PM: example of curvature (space curve), id=7624 -- WP guess: example of curvature (space curve) -- Status:

• PM: expressions for curvature and torsion, id=7567 -- WP guess: expressions for curvature and torsion -- Status:

• PM: famous curves, id=7073 -- WP guess: famous curves -- Status:

• PM: line in the plane, id=7108 -- WP guess: line in the plane -- Status:

• PM: Mean Curvature, id=7392 -- WP guess: Mean Curvature -- Status:

• PM: Serret-Frenet equations in \mathbb{R}^2, id=7072 -- WP guess: Serret-Frenet equations in \mathbbR^2 -- Status:

• PM: sinusoid, id=7101 -- WP guess: sinusoid -- Status:

• PM: circle of curvature, id=9277^new! -- WP guess: circle of curvature -- Status:

• PM: curvature determines the curve, id=9353^new! -- WP guess: curvature determines the curve -- Status:

• PM: curvature of a circle, id=7820^new! -- WP guess: curvature of a circle -- Status:

• PM: curvature of Nielsen's spiral, id=9350^new! -- WP guess: curvature of Nielsen's spiral -- Status:

• PM: easy calculation of the area of an ellipse, id=7689^new! -- WP guess: easy calculation of the area of an ellipse -- Status:

• PM: moving frame, id=8606^new! -- WP guess: moving frame -- Status:

• PM: order of contact, id=9278^new! -- WP guess: order of contact -- Status:

53A05 Surfaces in Euclidean space

• PM: Pappus's centroid theorem, id=7321 -- WP guess: Pappus's centroid theorem -- Status:

• PM: second fundamental form, id=7339 -- WP: second fundamental form -- Status: NM

linas 19:55, 5 March 2006 (UTC)

• PM: Gauss-Bonnet theorem, id=8807^new! -- WP guess: Gauss-Bonnet theorem -- Status:

• PM: Gauss-Bonnet theorem, id=8824^new! -- WP guess: Gauss-Bonnet theorem -- Status:

• PM: Gaussian curvature, id=9299^new! -- WP guess: Gaussian curvature -- Status:

• PM: shape operator, id=8132^new! -- WP guess: shape operator -- Status:

53A35 Non-Euclidean differential geometry

• PM: Smarandache geometries, id=5769 -- WP: Smarandache geometries -- Status: N

PM article is "not found", this PM link is broken? linas 19:37, 5 March 2006 (UTC)

• PM: 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: closed (differential form), id=3668 -- WP: closed (differential form) -- Status: A

Jtwdog 21:21, 21 October 2005 (UTC)

• PM: axial vector, id=7031 -- WP: axial vector -- Status: A

linas 19:09, 5 March 2006 (UTC)

• PM: circulation and vorticity, id=9611^new! -- WP guess: circulation and vorticity -- Status:

• PM: continuity equation, id=7944^new! -- WP guess: continuity equation -- Status:

• PM: derivation of the Laplacian from rectangular to spherical coordinates, id=9376^new! -- WP guess: derivation of the Laplacian from rectangular to spherical coordinates -- Status:

• PM: derivation of unit vectors in curvilinear coordinates, id=9321^new! -- WP guess: derivation of unit vectors in curvilinear coordinates -- Status:

• PM: motion of continuum, id=7889^new! -- WP guess: motion of continuum -- Status:

• PM: Reynolds transport theorem, id=8048^new! -- WP guess: Reynolds transport theorem -- Status:

• PM: time dilatation of a volume element, id=7911^new! -- WP guess: time dilatation of a volume element -- Status:

• PM: topics on vectors, id=7804^new! -- WP guess: topics on vectors -- Status:

• PM: vector fields: Lagrangian and Eulerian description, id=7863^new! -- WP guess: vector fields: Lagrangian and Eulerian description -- Status:

53A55 Differential invariants (local theory), geometric objects

• PM: Riemann curvature tensor, id=8592^new! -- WP guess: Riemann curvature tensor -- Status:

53A99 Miscellaneous

• PM: Euclidean distance, id=1318 -- WP guess: Euclidean distance -- Status:

• PM: some structures on \mathbb{R}^n, id=5419 -- WP guess: some structures on \mathbbR^n -- Status:

53B05 Linear and affine connections

• PM: affine connection, id=6191 -- WP: affine connection -- Status: NM

linas 04:23, 11 Apr 2005 (UTC)

• PM: conjugate points, id=6159 -- WP guess: conjugate points -- Status:

• PM: connection, id=2880 -- WP: connection -- Status: NM

The PM article is quite a bit larger linas 04:25, 11 Apr 2005 (UTC)

• PM: Levi-Civita connection, id=4765 -- WP: Levi-Civita connection -- Status: A

linas 04:29, 11 Apr 2005 (UTC)

• PM: Riemann normal coordinates, id=6157 -- WP guess: Riemann normal coordinates -- Status:

• PM: vector field along a curve, id=4755 -- WP guess: vector field along a curve -- Status:

53B20 Local Riemannian geometry

• PM: Euclidean space as a manifold, id=7355 -- WP guess: Euclidean space as a manifold -- Status:

• PM: first fundamental form, id=7332 -- WP guess: first fundamental form -- Status:

• PM: first order operators in Riemannian geometry, id=7325 -- WP guess: first order operators in Riemannian geometry -- Status:

• PM: formulas in Riemannian geometry, id=7446 -- WP guess: formulas in Riemannian geometry -- Status:

• PM: sectional curvature, id=7907^new! -- WP guess: sectional curvature -- Status:

• PM: sectional curvature determines Riemann curvature tensor, id=7924^new! -- WP guess: sectional curvature determines Riemann curvature tensor -- Status:

53B21 Methods of Riemannian geometry

• PM: Hodge star operator, id=4120 -- WP: Hodge star operator -- Status: NM

• PM: Riemannian manifold, id=3452 -- WP: Riemannian manifold -- Status: NM

53B99 Miscellaneous

• PM: 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: germ of smooth functions, id=3501 -- WP guess: germ of smooth functions -- Status:

• PM: Pfaff's problem, id=6210 -- WP guess: Pfaff's problem -- Status:

• PM: germ, id=9801^new! -- WP guess: germ -- Status:

53C17 Sub-Riemannian geometry

• PM: Sub-Riemannian manifold, id=4754 -- WP: Sub-Riemannian manifold -- Status: A

linas 04:48, 11 Apr 2005 (UTC)

53C20 Global Riemannian geometry, including pinching

• PM: sphere theorem from global differential geometry, id=7905^new! -- WP guess: sphere theorem from global differential geometry -- Status:

53C22 Geodesics

• PM: affine parameter, id=6164 -- WP guess: affine parameter -- Status:

• PM: geodesic, id=5513 -- WP: geodesic -- Status: A

linas 04:33, 11 Apr 2005 (UTC)

• PM: geodesic triangle, id=9510^new! -- WP guess: geodesic triangle -- Status:

53C26 Hyper-Kähler and quaternionic Kähler geometry, special geometry

• PM: hyperkähler manifold, id=7813^new! -- WP guess: hyperkähler manifold -- Status:

53C42 Immersions (minimal, prescribed curvature, tight, etc.)

• PM: Nash isometric embedding theorem, id=7569 -- WP: Nash isometric embedding theorem -- Status: NC

linas 20:06, 5 March 2006 (UTC)

53C60 Finsler spaces and generalizations (areal metrics)

• PM: spray space, id=7372 -- WP: spray space -- Status: NC

linas 20:05, 5 March 2006 (UTC)

53D05 Symplectic manifolds, general

• PM: almost complex structure, id=3739 -- WP: almost complex structure -- Status: A

linas 17:45, 5 March 2006 (UTC)

• PM: coadjoint orbit, id=4760 -- WP: coadjoint orbit -- Status: NM

linas 17:49, 5 March 2006 (UTC)

• PM: Darboux's Theorem (symplectic geometry), id=3738 -- WP: Darboux's theorem -- Status: A

linas 18:15, 5 March 2006 (UTC)

• PM: examples of symplectic manifolds, id=3672 -- WP: symplectic manifold -- Status: NM

linas 18:19, 5 March 2006 (UTC)

• PM: Hamilton equations, id=6410 -- WP: Hamilton's equations -- Status: NM

linas 18:29, 5 March 2006 (UTC)

• PM: Hamiltonian vector field, id=3706 -- WP: Hamiltonian vector field -- Status: A

Jtwdog 21:37, 21 October 2005 (UTC)

• PM: 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. linas 17:09, 5 March 2006 (UTC)

• PM: isotropic submanifold, id=3670 -- WP: isotropic submanifold -- Status: NC

current WP article is a redirect. linas 18:33, 5 March 2006 (UTC)

• PM: lagrangian submanifold, id=3671 -- WP: lagrangian submanifold -- Status: A

PM article is a stub, WP article is redirect.linas 18:36, 5 March 2006 (UTC)

• PM: Moser's theorem, id=3806 -- WP: Moser's theorem -- Status: NC

linas 18:38, 5 March 2006 (UTC)

• PM: Poisson bracket, id=6412 -- WP: Poisson bracket -- Status: A

linas 20:03, 5 March 2006 (UTC)

• PM: Poisson ring, id=6414 -- WP: Poisson ring -- Status: C

linas 04:54, 11 Apr 2005 (UTC)

linas 17:06, 5 March 2006 (UTC)

• PM: proof of Darboux's Theorem (symplectic geometry), id=5589 -- WP: Darboux's Theorem -- Status: N

added ref to WP article. linas 21:07, 5 March 2006 (UTC)

• PM: 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. linas 04:53, 11 Apr 2005 (UTC)

• PM: symplectic matrix, id=4140 -- WP: symplectic matrix -- Status: A

linas 04:53, 11 Apr 2005 (UTC)

• PM: symplectic vector field, id=3705 -- WP: symplectic vector field -- Status: M

linas 18:53, 5 March 2006 (UTC)

• PM: symplectic vector space, id=4138 -- WP: symplectic vector space -- Status: A

linas 18:55, 5 March 2006 (UTC)

• PM: Examples of lagrangian submanifolds, id=7099 -- WP: Lagrangian submanifold -- Status: NM

linas 19:07, 5 March 2006 (UTC)

• PM: 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. linas 19:05, 5 March 2006 (UTC)

• PM: concepts in symplectic geometry, id=6423^new! -- WP guess: concepts in symplectic geometry -- Status:

• PM: every symplectic manifold has even dimension, id=7685^new! -- WP guess: every symplectic manifold has even dimension -- Status:

53D10 Contact manifolds, general

• PM: contact manifold, id=4409 -- WP: contact manifold -- Status: NM

linas 19:29, 5 March 2006 (UTC)

53D20 Momentum maps; symplectic reduction

• PM: momentum map, id=3718 -- WP: momentum map -- Status: A

linas 19:17, 5 March 2006 (UTC)

53D99 Miscellaneous

• PM: \mathbb{C} as a Kähler manifold, id=7733^new! -- WP guess: \mathbbC as a Kähler manifold -- Status:

• PM: a Kähler manifold is symplectic, id=8203^new! -- WP guess: a Kähler manifold is symplectic -- Status:

• PM: Kähler manifold, id=7673^new! -- WP guess: Kähler manifold -- Status:

• PM: Kähler potential, id=8740^new! -- WP guess: Kähler potential -- Status:

53Z05 Applications to physics

• PM: Minkowski space, id=8393^new! -- WP guess: Minkowski space -- Status:

• PM: pseudo-Riemannian manifold, id=7688^new! -- WP guess: pseudo-Riemannian manifold -- Status: