isometry group

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

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

is that subgroup of the group of all diffeomorphisms $\phi : X \to X$ that are isometries: which preserve the metric $g$ in that

$\phi^* g = g
\,.$

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

- The isometry group of Minkowski space is the Poincaré group.

Created on August 22, 2011 16:22:50
by Urs Schreiber
(82.113.99.25)