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COMPLETE CMC HYPERSURFACES IN THE HYPERBOLIC SPACE WITH PRESCRIBED GAUSS MAPPING.
- Source :
-
Proceedings of the American Mathematical Society . 2014, Vol. 142 Issue 10, p3597-3604. 8p. - Publication Year :
- 2014
-
Abstract
- Our aim in this paper is to show that a complete hypersurface x : Mn → ℍn+1 immersed with constant mean curvature into the hyperbolic space ℍn+1 is totally umbilical provided that its Gauss mapping ν has some suitable behavior. In this setting, our first result requires that the image ν(M) lies in a totally umbilical spacelike hypersurface of the de Sitter space Sn+1 1 , while in our second one we suppose that Mn has scalar curvature bounded from below and that ν(M) is contained in the closure of a domain enclosed by a totally umbilical spacelike hypersurface of Sn+1 1 determined by some vector a of the Minkowski space Ln+2, with the tangential component of a with respect to Mn having Lebesgue integrable norm. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CURVATURE
*CALCULUS
*HYPERSURFACES
*HYPERBOLIC spaces
*HYPERBOLIC groups
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 142
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 125284850
- Full Text :
- https://doi.org/10.1090/S0002-9939-2014-12118-6