Characterizations of the Calabi Product of Hyperbolic Affine Hyperspheres

Abstract.

There exists a well known construction which allows to associate with two hyperbolic affine hyperspheres $f_{i} : M^{n_{i}}_{i} \rightarrow {\mathbb{R}}^{n_{i}+1}$ a new hyperbolic affine hypersphere immersion of $I \times M_{1} \times M_{2}$ into ${\mathbb{R}}^{n_{1}+n_{2}+2}$. In this paper we deal with the inverse problem: how to determine from properties of the difference tensor whether a given hyperbolic affine hypersphere immersion of a manifold $M^{n} \rightarrow R^{n+1}$ can be decomposed in such a way.