MAXIMAL SPACE-LIKE HYPERSURFACES IN H14(-1) WITH ZERO GAUSS-KRONECKER CURVATURE

Abstract

In this paper, we study complete maximal space-like hypersurfaces with constant Gauss-Kronecker curvature in an antide Sitter space <TEX>$H_1^4(-1)$</TEX>. It is proved that complete maximal spacelike hypersurfaces with constant Gauss-Kronecker curvature in an anti-de Sitter space <TEX>$H_1^4(-1)$</TEX> are isometric to the hyperbolic cylinder <TEX>$H^2(c1){\times}H^1(c2)$</TEX> with S = 3 or they satisfy <TEX>$S{\leq}2$</TEX>, where S denotes the squared norm of the second fundamental form.