A bernstein property of affine maximal hypersurfaces

Let x: M --> A(n+1) be a locally strongly convex hypersurface, given as a graph of a locally strongly convex function x(n+1) = f ( x(1),...,x(n)) defined in a domain Omega subset of A(n). We introduce a Riemannian metric G(#) = Sigma(partial derivative(2) f /partial derivativex(i) partial derivativex(j)) dx(i) dx(j) on M. In this paper, we investigate the affine maximal hypersurfaces which are complete with respect to the metric G(#) and prove a Bernstein property for the affine maximal hypersurfaces.