A characterisation of the Calabi product of hyperbolic affine spheres

Details A characterisation of the Calabi product of hyperbolic affine spheres A characterisation of the Calabi product of hyperbolic affine spheres

2007-12-07

arxiv.org/abs/0712.1073v1

Mathematics

Differential Geometry

14pages

Scientific paper

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.

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