Gauss's lemma (Riemannian geometry)
id:
gauss-s-lemma-riemannian-geometry-191-10864729
title:
Gauss's lemma (Riemannian geometry)
text:
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 t
brand slug:
wiki
category slug:
encyclopedia
description:
Theorem in manifold theory
original url:
https://en.wikipedia.org/wiki/Gauss%27s_lemma_(Riemannian_geometry)
date created:
date modified:
2023-12-17T01:20:29Z
main entity:
{"identifier":"Q3229339","url":"https://www.wikidata.org/entity/Q3229339"}
image:
fields total:
13
integrity:
14