New characterizations for hyperbolic cylinders in anti-de Sitter spaces

In this paper we study complete maximal spacelike hypersurfaces in anti-de Sitter space H1n+1 with either constant scalar curvature or constant non-zero Gauss–Kronecker curvature. We characterize the hyperbolic cylinders Hm(c1)×Hn−m(c2),1≤m≤n−1, as the only such hypersurfaces with (n−1) principal cu...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2012-09, Vol.393 (1), p.166-176
Main Authors: Chaves, R.M.B., Sousa, L.A.M., Valério, B.C.
Format: Article
Language:English
Subjects:
Anti-de Sitter space
Complete spacelike hypersurfaces
Gauss–Kronecker curvature
Scalar curvature
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we study complete maximal spacelike hypersurfaces in anti-de Sitter space H1n+1 with either constant scalar curvature or constant non-zero Gauss–Kronecker curvature. We characterize the hyperbolic cylinders Hm(c1)×Hn−m(c2),1≤m≤n−1, as the only such hypersurfaces with (n−1) principal curvatures with the same sign everywhere. In particular we prove that a complete maximal spacelike hypersurface in H15 with negative constant Gauss–Kronecker curvature is isometric to H1(c1)×H3(c2).
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.03.043