𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On totally umbilic submanifolds of semi-Riemannian manifolds

✍ Scribed by Volker Perlick

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
120 KB
Volume
63
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

✦ Synopsis

The notion of being totally umbilic is considered for non-degenerate and degenerate submanifolds of semi-Riemannian 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.

πŸ“œ SIMILAR VOLUMES

On gradient dynamical system on semi-Rie
On gradient dynamical system on semi-Riemannian manifolds
✍ Jens Chr. Larsen πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science 🌐 English βš– 805 KB

We considergradient dynamical systems on a serni-Riemannian manifold of arbitrary index. The main point of the paper is the introduction of the concepts causality subsets, causality function and sector stability. As a main application we provide conditions assuring, that the non wandering points are