On the Gauss image of a spacelike hypersurface with constant mean curvature in Minkowski space

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Abstract

To generalize Bernstein's theorem on minimal surfaces Chern [5] proposed to study the distribution of normals to complete constant mean curvature hypersurface in Euclidean space. In this direction there is a remarkable theorem given by Hoffman, Osserman and Schoen [7]. The author also considered more general cases of this kind of problem in a previous work [2]. In [10] Palmer studied the analogous problem in the ambient Minkowski space. Let M be an oriented spacel~ke hypersurface in a Minkowski space ~7+t. Let be the timelike unit normal vector field to M in R~ '+1. For any point p e M l ~ ( p ) [ 2 = 1 . By parallel translation to the origin in ~7 § ~ we can regard ~ ( p ) as a point in the n-dimensional hyperbolic space H ( 1) which is canonically embedded in ~7+ 1. In such a way we have the Gauss map y : M ~ H ( 1). Palmer proved the following result:

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