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- Title
CHARACTERIZATIONS OF LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN EINSTEIN SPACETIMES.
- Authors
DE LIMA, HENRIQUE F.; DE LIMA, JOSEÍLSON R.
- Abstract
Our purpose is to study the geometry of linear Weingarten spacelike hypersurfaces immersed in a locally symmetric Einstein spacetime, whose sectional curvature is supposed to obey some standard restrictions. In this setting, by using as main analytical tool a generalized maximum principle for complete non-compact Riemannian manifolds, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures, one of which is simple. Applications to the de Sitter space are given.
- Subjects
LINEAR systems; HYPERSURFACES; SPACETIME; MATHEMATICAL symmetry; CURVATURE; RIEMANNIAN manifolds; GENERALIZATION
- Publication
Glasgow Mathematical Journal, 2013, Vol 55, Issue 3, p567
- ISSN
0017-0895
- Publication type
Article
- DOI
10.1017/S0017089512000754