Exponential map (Riemannian geometry)

In Riemannian geometry, an exponential map is a map from a subset of a tangent space T_pM 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.