Hyperbolic Relative Hyperspheres with Li-normalization

Abstract

Consider a graph hypersurface $$M=\{(x_1,\ldots,x_n,f(x_1,\ldots,x_n))\;\;|\;\; (x_1,\ldots,x_n)\in \Omega\}$$ where f is a strictly convex function defined on a convex domain Ω in real affine space An. Assume that the hypersurface has a Li-normalization. We study hyperbolic affine hyperspheres with respect to this relative normalization and classify the subclass which is Euclidean complete.