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Exponential mapIn 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 certain metrics on Lie groups, in the matrix representation of Lie group and its tangent Lie algebra. 
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Exponential map".