Complete manifold
id:
complete-manifold-184-11868604
title:
Complete manifold
text:
In mathematics, a complete manifold M is a (pseudo-) Riemannian manifold for which, starting at any point p, there are straight paths extending infinitely in all directions. Formally, a manifold M is (geodesically) complete if for any maximal geodesic ℓ : I → M, it holds that I =. A geodesic is maximal if its domain cannot be extended. Equivalently, M is (geodesically) complete if for all points p ∈ M, the exponential map at p is defined on T p M, the entire tangent space at p.
brand slug:
wiki
category slug:
encyclopedia
description:
Riemannian manifold in which geodesics extend infinitely in all directions
original url:
https://en.wikipedia.org/wiki/Complete_manifold
date created:
2006-09-06T23:50:15Z
date modified:
2024-09-07T13:30:18Z
main entity:
{"identifier":"Q5533982","url":"https://www.wikidata.org/entity/Q5533982"}
image:
fields total:
13
integrity:
15