Geometry of manifolds in the euclidian space and in the Minkowski space
Algebraic, topological and analytical techniques in differential geometry and geom...
Isometric immersions of (intrinsically) homogeneous manifolds
| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Libre Bruxelles, Geometrie Differentielle, B-2131050 Brussels - Belgium
[2] Hellen Mil Acad, Fac Math & Engn Sci, Attiki - Greece
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS; v. 42, p. 1-14, OCT 2015. |
| Web of Science Citations: | 2 |
| Abstract | |
The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel. (C) 2015 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 11/21362-2 - Group actions, submanifold theory and global analysis in Riemannian and pseudo-Riemannian geometry |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |