page_title: Exponential map (Riemannian geometry)
hierarchical_section_title: Exponential map (Riemannian geometry)
caption_attribution_description: English: polar azimuthal equidistant projection of the earth (centered to north pole) Deutsch: polare äquidistante Azimutalprojektion der Erde (zentriert auf den Nordpol) Français&#160;: Projection cartographique azimuthale équidistante polaire (centrée sur le Pôle Nord)
context_page_description: In Riemannian geometry, an exponential map is a map from a subset of a tangent space TₚM of a Riemannian manifold M to M itself. The Riemannian metric determines a canonical affine connection, and the exponential map of the Riemannian manifold is given by the exponential map of this connection.
context_section_description: 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.
caption: The exponential map of the Earth as viewed from the north pole is the polar azimuthal equidistant projection in cartography.
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