About: Exponential map (Riemannian geometry)

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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.

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rdf:type	software
rdfs:label	Exponential map (Riemannian geometry) (en) Экспоненциальное отображение (ru) 指數映射 (黎曼幾何) (zh)
rdfs:comment	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. (en) Экспоненциальное отображение — далеко[уточнить] идущее обобщение экспоненциальной функции в римановой геометрии. Для риманова многообразия экспоненциальное отображение действует из касательного расслоения в само многообразие . Экспоненциальное отображение обычно обозначается ,а его сужение на касательное пространство в точке обозначается и называется экспоненциальным отображением в точке . (ru) 黎曼几何中，指數映射（英語：exponential map）是由某（偽）黎曼流形切空间的子集，到本身的映射。（伪）黎曼度量對應某個典範仿射聯絡，而（伪）黎曼流形的指数映射就是这个聯絡的指数映射。直觀理解，由起點出發，以揀選切向量為速度，沿流形上的「直線」行單位時間，到達的終點就是。 (zh)
foaf:depiction
dcterms:subject	Differential geometry Riemannian geometry
Wikipage page ID	276548 (xsd:integer)
Wikipage revision ID	1113780149 (xsd:integer)
Link from a Wikipage to another Wikipage	Hopf–Rinow theorem Curvature of Riemannian manifolds Cut locus (Riemannian manifold) Double tangent bundle Inverse function theorem Lie group Positive real numbers Differential geometry Compact space Tangent bundle Gauss's lemma (Riemannian geometry) Gaussian curvature Geodesic Lie algebra Gauss's lemma (disambiguation) Straight line Tangent space Affine connection American Mathematical Society Diffeomorphism Foundations of Differential Geometry Graduate Studies in Mathematics List of exponential topics Pseudo-Riemannian manifold Riemannian geometry Riemannian manifold Riemannian geometry Differentiable manifold Picard–Lindelöf theorem Identity function Metric space Ordinary differential equation Exponential map (Lie theory) Injectivity radius Tangent vector Sectional curvature Geodesic normal coordinates
sameAs	Exponential map (Riemannian geometry) Exponential map (Riemannian geometry) Exponential map (Riemannian geometry) Exponential map (Riemannian geometry) Exponential map (Riemannian geometry) Exponential map (Riemannian geometry)
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thumbnail	wiki-commons:Special:FilePath/Azimuthal_Equidistant_N90.jpg?width=300
id	p/e036930 (en)
title	Exponential mapping (en)
has abstract	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. (en) Экспоненциальное отображение — далеко[уточнить] идущее обобщение экспоненциальной функции в римановой геометрии. Для риманова многообразия экспоненциальное отображение действует из касательного расслоения в само многообразие . Экспоненциальное отображение обычно обозначается ,а его сужение на касательное пространство в точке обозначается и называется экспоненциальным отображением в точке . (ru) 黎曼几何中，指數映射（英語：exponential map）是由某（偽）黎曼流形切空间的子集，到本身的映射。（伪）黎曼度量對應某個典範仿射聯絡，而（伪）黎曼流形的指数映射就是这个聯絡的指数映射。直觀理解，由起點出發，以揀選切向量為速度，沿流形上的「直線」行單位時間，到達的終點就是。 (zh)
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foaf:isPrimaryTopicOf	wikipedia-en:Exponential_map_(Riemannian_geometry)
is Link from a Wikipage to another Wikipage of	Rodrigues' rotation formula List of differential geometry topics Hopf–Rinow theorem Curvature of Riemannian manifolds Cut locus (Riemannian manifold) Levi-Civita parallelogramoid Computational anatomy Convenient vector space Generator (mathematics) Normal coordinates Gauss's lemma (Riemannian geometry) Geodesic Geodesic manifold Logarithm Six-dimensional space Tangent space Affine connection Diffeomorphism Glossary of Riemannian and metric geometry Hilbert's theorem (differential geometry) List of exponential topics Riemannian geometry Riemannian manifold Tetrad formalism Differential geometry of surfaces

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