nLab
isometry group

Context

Riemannian geometry

Differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

Theorems

Applications

Contents

Definition

For (X,g)(X,g) a Riemannian manifold or pseudo-Riemannian manifold its isometry group

Iso(X,g)Diff(X) Iso(X,g) \subset Diff(X)

is that subgroup of the group of all diffeomorphisms ϕ:XX\phi : X \to X that are isometries: which preserve the metric gg in that

ϕ *g=g. \phi^* g = g \,.

Properties

Killing vectors

The Lie algebra of Iso(X,g)Iso(X,g) is spanned by the Killing vectors of (X,g)(X,g).

Examples

Revised on March 25, 2015 12:42:29 by Urs Schreiber (195.113.30.252)