Exponential map (Riemannian geometry)

For other uses, see Exponential map.
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 TpM 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.