Rauch comparison theorem
id:
rauch-comparison-theorem-254-7795083
title:
Rauch comparison theorem
text:
In Riemannian geometry, the Rauch comparison theorem, named after Harry Rauch, who proved it in 1951, is a fundamental result which relates the sectional curvature of a Riemannian manifold to the rate at which geodesics spread apart. Intuitively, it states that for positive curvature, geodesics tend to converge, while for negative curvature, geodesics tend to spread. The statement of the theorem involves two Riemannian manifolds, and allows to compare the infinitesimal rate at which geodesics sp
brand slug:
wiki
category slug:
encyclopedia
description:
Relates sectional curvature of a Riemannian manifold to the rate geodesics spread apart
original url:
https://en.wikipedia.org/wiki/Rauch_comparison_theorem
date created:
date modified:
2024-02-29T18:54:59Z
main entity:
{"identifier":"Q7296106","url":"https://www.wikidata.org/entity/Q7296106"}
image:
fields total:
13
integrity:
14