New characterizations for hyperbolic cylinders in anti-de Sitter spaces

作者：Chaves R M B; Sousa L A M Jr^*; Valerio B C

来源：Journal of Mathematical Analysis and Applications, 2012, 393(1): 166-176.

DOI：10.1016/j.jmaa.2012.03.043

• Anti-de Sitter space
• Complete spacelike hypersurfaces
• Gauss-Kronecker curvature
• Scalar curvature

In this paper we study complete maximal spacelike hypersurfaces in anti-de Sitter space H-1(n+1) with either constant scalar curvature or constant non-zero Gauss-Kronecker curvature. We characterize the hyperbolic cylinders H-m(c(1)) x Hn-m(c(2)), 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 H-1(5) with negative constant Gauss-Kronecker curvature is isometric to H-1(c(1)) x H-3(c(2)).

• 出版日期2012-9-1