Totally geodesic hypersurfaces of four-dimensional generalized symmetric spaces |
| |
Authors: | Barbara De Leo Joeri Van der Veken |
| |
Institution: | 1. Dipartimento di Matematica “E. De Giorgi”, Università del Salento, Provinciale Lecce–Arnesano, 73100, Lecce, Italy 2. Department Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, Box 2400, 3001, Leuven, Belgium
|
| |
Abstract: | We prove that a four-dimensional generalized symmetric space does not admit any non-degenerate hypersurfaces with parallel second fundamental form, in particular non-degenerate totally geodesic hypersurfaces, unless it is locally symmetric. However, spaces which are known as generalized symmetric spaces of type C do admit non-degenerate parallel hypersurfaces and we verify that they are indeed symmetric. We also give a complete and explicit classification of all non-degenerate totally geodesic hypersurfaces of spaces of this type. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|