There exists a well known construction which allows to associate with two hyperbolic affine spheres $f_i: M_i^{ n_i} \to \mathbb R^{ n_i+1}$ a new hyperbolic affine sphere immersion of $I \times M_1 \times M_2$ into $\mathbb R^{ n_1+n_2+3}$. In this paper we deal with the inverse problem: how to determine from properties of the difference tensor whether a given hyperbolic affine sphere immersion of a manifold $M^n \to \mathbb R^{ n+1}$ can be decomposed in such a way.
Categories: math.DG