Flat manifold
id:
flat-manifold-174-3563830
title:
Flat manifold
text:
In mathematics, a Riemannian manifold is said to be flat if its Riemann curvature tensor is everywhere zero. Intuitively, a flat manifold is one that "locally looks like" Euclidean space in terms of distances and angles, e.g. the interior angles of a triangle add up to 180°. The universal cover of a complete flat manifold is Euclidean space. This can be used to prove the theorem of Bieberbach (1911, 1912) that all compact flat manifolds are finitely covered by tori; the 3-dimensional case was pr
brand slug:
wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Flat_manifold
date created:
2007-08-13T22:25:02Z
date modified:
2024-09-02T17:47:38Z
main entity:
{"identifier":"Q601110","url":"https://www.wikidata.org/entity/Q601110"}
image:
fields total:
13
integrity:
14