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单词 MorseFunction
释义

Morse function


Let M be a smooth manifoldMathworldPlanetmath. A critical pointMathworldPlanetmath of a map u:M at xM is called if the Hessian matrix Hu (in any local coordinate system) at x is non-degenerate.

A smooth functionMathworldPlanetmath u:M is called Morse if all its critical points are non-degenerate. Morse functions exist on any smooth manifold, and in fact form an open dense (http://planetmath.org/Dense) subset of smooth functions on M (this fact is often phrased “a generic smooth function is Morse”).

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更新时间:2025/5/4 12:01:11