Toponogov's theorem
id:
toponogov-s-theorem-279-17003188
title:
Toponogov's theorem
text:
In the mathematical field of Riemannian geometry, Toponogov's theorem is a triangle comparison theorem.
It is one of a family of comparison theorems that quantify the assertion that a pair of geodesics emanating from a point p spread apart more slowly in a region of high curvature than they would in a region of low curvature. Let M be an m-dimensional Riemannian manifold with sectional curvature K satisfying K ≥ δ . Let pqr be a geodesic triangle, i.e. a triangle whose sides are geodesics, in M,
brand slug:
wiki
category slug:
encyclopedia
description:
Triangle comparison theorem in Riemannian geometry
original url:
https://en.wikipedia.org/wiki/Toponogov%27s_theorem
date created:
date modified:
2023-08-12T00:27:11Z
main entity:
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fields total:
13
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14