### Context

#### Differential geometry

differential geometry

synthetic differential geometry

# Contents

## Idea

For $\left(X,g\right)$ a Riemannian manifold and $f:X\to ℝ$ a smooth function, let

$\nabla f:={g}^{-1}\left({d}_{\mathrm{dR}}f\right)\in \Gamma \left(TX\right)$\nabla f := g^{-1}(d_{dR} f) \in \Gamma(T X)

be the gradient vector field of $X$. The flow induced by this on $X$ is the gradient flow of $f$.

## Examples

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