A rigidity theorem for a space-like graph of higher codimension (Q1593646)

First the author considers a space-like graph with parallel mean curvature of arbitrary dimension and codimension in pseudo-Euclidean space. Using the fact that in this case the generalized Gauss map is a harmonic map from such graph into a specific Cartan-Hadamard manifold he proves a rigidity theorem. Next the author gives an estimate of the squared length of the second fundamental form in terms of the mean curvature and the diameter of the Gauss image for space-like submanifolds with parallel mean curvature. Moreover, he shows that an application of this estimate gives another proof of the main theorem.