On totally umbilic submanifolds of semi-Riemannian manifolds

Details On totally umbilic submanifolds of semi-Riemannian manifolds On totally umbilic submanifolds of semi-Riemannian manifolds

2005-12-11

arxiv.org/abs/gr-qc/0512066v1

Nonlinear Analysis 63/5-7 (2005) e511-e518

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages; written version of talk given at World Congress on Nonlinear Analysis 2004, Orlando, Florida

Scientific paper

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.

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