Isometric splitting for actions of simple Lie groups on pseudo-Riemannian manifolds (Q2387797)

The preservation of a given geometric structure under the action of Lie groups is a fundamental problem in geometry. Of particularly interest is the case of a simple, connected and compact group \(G\), respectively, pseudo-Riemannian structure on a connected manifold \(M\). The paper under review is devoted to the above case where in addition \(M\) has finite volume. The main result yields a splitting of the metric on \(M\) that involves natural metrics on \(G\). The well-known warped product metrics are produced in this way, for suitable \(G\).