Exponential map

This page is about the exponential map in differential geometry. For discrete dynamical systems, see Exponential map (discrete dynamical systems).

The exponential map of the Earth as viewed from the north pole is the polar azimuthal equidistant projection in cartography.

In differential geometry, the exponential map is a generalization of the ordinary exponential function of mathematical analysis to all differentiable manifolds with an affine connection. Two important special cases of this are

• The exponential map for a manifold with a Riemannian metric, and
• The exponential map from a Lie algebra to a Lie group (for the latter see Exponential map (Lie theory).)