Property Of Complete Affine Maximal Hypersurfaces

Let x : M → An+l be a locally strongly convex hypersurface,given by a strictly convex function xn+1= f(x1 ......, xn) defined in aconvex domain fi C ^4" we consider the Blaschke metric G = . In this paper, we will first introduce the general theory ofcompleteness.Then we will investigate the affine maximal hypersurface, whichis complete with respect to the metric G, and prove some results for the affinemaximal hypersurfaces.