Exponential map Guide, Meaning , Facts, Information and Description
In differential geometry, the exponential map is the map from (a subset of) the tangent space of a Riemannian manifold M to M itself. It is defined in the following way:
For there is a unique geodesic such that having a tangent vector . Then
The name comes from the fact that it coincides with exponentiation of matrices in the case of bi-invariant metrics on Lie groups, when one is using a matrix representation of the group, and its Lie algebra as tangent space at the identity.
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