On totally umbilic submanifolds of semi-Riemannian manifolds
Abstract
Description
The notion of being totally umbilic is considered for non-degenerate and degenerate submanifolds of semi-Riemanian manifolds. After some remarks on the general case, timelike and lightlike totally umbilic submanifolds of Lorentzian manifolds are discussed, along with their physical interpretation in view of general relativity. In particular, the mathematical notion of totally umbilic submanifolds is linked to the notions of photon surfaces and of null strings which have been used in the physics literature.
7 pages; written version of talk given at World Congress on Nonlinear Analysis 2004, Orlando, Florida
7 pages; written version of talk given at World Congress on Nonlinear Analysis 2004, Orlando, Florida