A rigidity theorem for a space-like graph¶of higher codimension

Abstract

We prove a rigidity theorem for a space-like graph with parallel mean curvature of arbitrary dimension and codimension in pseudo-Euclidean space via properties of its harmonic Gauss map. We also give an estimate of the squared norm of the second fundamental form in terms of the mean curvature and the image diameter under the Gauss map for space-like submanifolds with parallel mean curvature in pseudo-Euclidean space. The estimate also implies the former theorem.