Theorem of the three geodesics
id:
theorem-of-the-three-geodesics-292-17643761
title:
Theorem of the three geodesics
text:
In differential geometry the theorem of the three geodesics, also known as Lyusternik–Schnirelmann theorem, states that every Riemannian manifold with the topology of a sphere has at least three simple closed geodesics. The result can also be extended to quasigeodesics on a convex polyhedron, and to closed geodesics of reversible Finsler 2-spheres. The theorem is sharp: although every Riemannian 2-sphere contains infinitely many distinct closed geodesics, only three of them are guaranteed to hav
brand slug:
wiki
category slug:
encyclopedia
description:
Every Riemannian manifold with the topology of a sphere has at least three closed geodesics
original url:
https://en.wikipedia.org/wiki/Theorem_of_the_three_geodesics
date created:
date modified:
2023-11-29T10:53:20Z
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