Null and infinitesimal isotropy in semi-Riemannian geometry
The earlier concepts of infinitesimal spatial or null isotropy of a semi- Riemannian manifold are generalized to infinitesimal isotropy with respect to an orthogonal decomposition of the tangent space. Sufficient conditions on \((M,g)\) to be a warped product are given in terms of the new notion. The authors also define null isotropy, which turns out to be essentially conformal flatness. The concepts apply to cosmological and black hole solutions of general relativity.
scientific article; zbMATH DE number 569286