nLab
gradient flow

Context

Differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

Theorems

Applications

Contents

Idea

For (X,g)(X,g) a Riemannian manifold and f:Xf : X \to \mathbb{R} a smooth function, let

f:=g 1(d dRf)Γ(TX) \nabla f := g^{-1}(d_{dR} f) \in \Gamma(T X)

be the gradient vector field of XX. The flow induced by this on XX is the gradient flow of ff.

Examples

Created on August 26, 2011 20:21:33 by Urs Schreiber (89.204.137.99)