Exponential map (Riemannian geometry)

In Riemannian geometry, an exponential map is a map from a subset of a tangent space T p M {\displaystyle T_{p}M} of a Riemannian manifold (or pseudo-Riemannian manifold) M {\displaystyle M} to M {\displaystyle 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.

Source: Wikipedia — Exponential map (Riemannian geometry) (CC BY-SA 4.0)