Immersion (mathematics)
id:
immersion-mathematics-174-16644781
title:
Immersion (mathematics)
text:
In mathematics, an immersion is a differentiable function between differentiable manifolds whose differential pushforward is everywhere injective. Explicitly, f : M → N is an immersion if
- D p f : T p M → T f N is an injective function at every point p of M. Equivalently, f is an immersion if its derivative has constant rank equal to the dimension of M:
- rank D p f = dim M. The function f itself need not be injective, only its derivative must be.
brand slug:
wiki
category slug:
encyclopedia
description:
Differentiable function whose derivative is everywhere injective
original url:
https://en.wikipedia.org/wiki/Immersion_(mathematics)
date created:
2006-09-14T20:24:34Z
date modified:
2024-09-03T09:43:56Z
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image:
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fields total:
13
integrity:
16