Editing Exponential map (Riemannian geometry) (section)

{{Short description|Map from tangent space to the manifold}}
{{Other uses|Exponential map (disambiguation){{!}}Exponential map}}

[[File:Azimuthal Equidistant N90.jpg|thumb|right|The exponential map of the Earth as viewed from the north pole is the polar [[azimuthal equidistant projection]] in cartography.]]
In [[Riemannian geometry]], an '''exponential map''' is a map from a subset of a [[tangent space]] T<sub>''p''</sub>''M'' of a [[Riemannian manifold]] (or [[pseudo-Riemannian manifold]]) ''M'' to ''M'' itself.  The (pseudo) Riemannian metric determines a canonical affine connection, and the exponential map of the (pseudo) Riemannian manifold is given by the exponential map of this connection.