Open Access
With zero gauss-kronecker curvature
Qing-Ming Cheng,Young Jin Suh +1 more
TLDR
In this article, complete maximal space-like hypersurfaces with constant Gauss-Kronecker curvature in an anti-de Sitter space H 4 (i1) are proved isometric to the hyperbolic cylinder H 2 (c1)£H 1 (c2) with S = 3 or they satisfy S • 2, where S denotes the squared norm of the second fundamental form.Abstract:
In this paper, we study complete maximal space-like hypersurfaces with constant Gauss-Kronecker curvature in an anti- de Sitter space H 4(i1). It is proved that complete maximal space- like hypersurfaces with constant Gauss-Kronecker curvature in an anti-de Sitter space H 4 (i1) are isometric to the hyperbolic cylinder H 2 (c1)£H 1 (c2) with S = 3 or they satisfy S • 2, where S denotes the squared norm of the second fundamental form.read more
References
More filters
Book
Semi-Riemannian Geometry With Applications to Relativity
TL;DR: In this article, the authors introduce Semi-Riemannian and Lorenz geometries for manifold theory, including Lie groups and Covering Manifolds, as well as the Calculus of Variations.
Journal ArticleDOI
Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
Shiu-Yuen Cheng,Shing-Tung Yau +1 more
Journal ArticleDOI
Isometric immersions of Riemannian manifolds
Journal ArticleDOI
On spacelike hypersurfaces with constant mean curvature in the de Sitter space
TL;DR: Soit N=(N n+1 (c),g) une variete de Lorentz a (n+1) dimensions de courbure constante positive c. Alors M est totalement ombilicale as discussed by the authors.