Almost flat manifold
id:
almost-flat-manifold-246-10484063
title:
Almost flat manifold
text:
In mathematics, a smooth compact manifold M is called almost flat if for any ε > 0 there is a Riemannian metric g ε on M such that diam ≤ 1 and g ε is ε -flat, i.e. for the sectional curvature of K g ε we have | K g ϵ | < ε . Given n, there is a positive number ε n > 0 such that if an n-dimensional manifold admits an ε n -flat metric with diameter ≤ 1 then it is almost flat. On the other hand, one can fix the bound of sectional curvature and get the diameter going to zero, so the almost-flat man
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wiki
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encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Almost_flat_manifold
date created:
date modified:
2024-03-29T19:14:32Z
main entity:
{"identifier":"Q4734002","url":"https://www.wikidata.org/entity/Q4734002"}
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13
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13