Exponential map

• exponential map for a manifold with a Riemannian metric,
• exponential map from a Lie algebra to a Lie group,
• More generally, in a manifold with an affine connection,, where is a geodesic with initial velocity X, is sometimes also called the exponential map. The above two are special cases of this with respect to appropriate affine connections.
• Euler's formula forming the unit circle in the complex plane.