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 ( subset of smooth functions on M (this fact is often phrased “a generic smooth function is Morse”).

Title Morse function
Canonical name MorseFunction
Date of creation 2013-03-22 13:53:15
Last modified on 2013-03-22 13:53:15
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 8
Author bwebste (988)
Entry type Definition
Classification msc 58E05
Defines non-degenerate critical point