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- Gauss's_lemma_(Riemannian_geometry) abstract "In Riemannian geometry, Gauss's lemma asserts that any sufficiently small sphere centered at a point in a Riemannian manifold is perpendicular to every geodesic through the point. More formally, let M be a Riemannian manifold, equipped with its Levi-Civita connection, and p a point of M. The exponential map is a mapping from the tangent space at p to M:which is a diffeomorphism in a neighborhood of zero. Gauss' lemma asserts that the image of a sphere of sufficiently small radius in TpM under the exponential map is perpendicular to all geodesics originating at p. The lemma allows the exponential map to be understood as a radial isometry, and is of fundamental importance in the study of geodesic convexity and normal coordinates.".
- Gauss's_lemma_(Riemannian_geometry) thumbnail Gauss_lemma_radial_isometry.png?width=300.
- Gauss's_lemma_(Riemannian_geometry) wikiPageID "15585793".
- Gauss's_lemma_(Riemannian_geometry) wikiPageRevisionID "560659814".
- Gauss's_lemma_(Riemannian_geometry) hasPhotoCollection Gauss's_lemma_(Riemannian_geometry).
- Gauss's_lemma_(Riemannian_geometry) subject Category:Articles_containing_proofs.
- Gauss's_lemma_(Riemannian_geometry) subject Category:Lemmas.
- Gauss's_lemma_(Riemannian_geometry) subject Category:Theorems_in_Riemannian_geometry.
- Gauss's_lemma_(Riemannian_geometry) type Abstraction100002137.
- Gauss's_lemma_(Riemannian_geometry) type Communication100033020.
- Gauss's_lemma_(Riemannian_geometry) type Lemma106751833.
- Gauss's_lemma_(Riemannian_geometry) type Lemmas.
- Gauss's_lemma_(Riemannian_geometry) type Message106598915.
- Gauss's_lemma_(Riemannian_geometry) type Proposition106750804.
- Gauss's_lemma_(Riemannian_geometry) type Statement106722453.
- Gauss's_lemma_(Riemannian_geometry) type Theorem106752293.
- Gauss's_lemma_(Riemannian_geometry) type TheoremsInRiemannianGeometry.
- Gauss's_lemma_(Riemannian_geometry) comment "In Riemannian geometry, Gauss's lemma asserts that any sufficiently small sphere centered at a point in a Riemannian manifold is perpendicular to every geodesic through the point. More formally, let M be a Riemannian manifold, equipped with its Levi-Civita connection, and p a point of M. The exponential map is a mapping from the tangent space at p to M:which is a diffeomorphism in a neighborhood of zero.".
- Gauss's_lemma_(Riemannian_geometry) label "Gauss's lemma (Riemannian geometry)".
- Gauss's_lemma_(Riemannian_geometry) label "Lemme de Gauss (géométrie riemannienne)".
- Gauss's_lemma_(Riemannian_geometry) sameAs Lemme_de_Gauss_(géométrie_riemannienne).
- Gauss's_lemma_(Riemannian_geometry) sameAs m.03mglqm.
- Gauss's_lemma_(Riemannian_geometry) sameAs Q3229339.
- Gauss's_lemma_(Riemannian_geometry) sameAs Q3229339.
- Gauss's_lemma_(Riemannian_geometry) sameAs Gauss's_lemma_(Riemannian_geometry).
- Gauss's_lemma_(Riemannian_geometry) wasDerivedFrom Gauss's_lemma_(Riemannian_geometry)?oldid=560659814.
- Gauss's_lemma_(Riemannian_geometry) depiction Gauss_lemma_radial_isometry.png.
- Gauss's_lemma_(Riemannian_geometry) isPrimaryTopicOf Gauss's_lemma_(Riemannian_geometry).
