Exponential map (Riemannian geometry)
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This article is about the exponential map in differential geometry. For discrete dynamical systems, see Exponential map (discrete dynamical systems). For the exponential map from a Lie algebra to a Lie group, see Exponential map (Lie theory).
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.