A characterisation of the Calabi product of hyperbolic affine spheres

2007/12/07 by Zejun Hu, Haizhong Li, Hu, Zejun +3
Mathematics · #53A15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53A15

paper · pdf · doi:10.48550/arxiv.0712.1073

14pages

arxiv created 2007/12/07 · openalex publication_date 2007/12/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There exists a well known construction which allows to associate with two hyperbolic affine spheres f_i: M_i^n_i → \mathbb R^n_i+1 a new hyperbolic affine sphere immersion of I × M₁ × M₂ into \mathbb R^n₁+n₂+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 Mⁿ → \mathbb Rⁿ⁺¹ can be decomposed in such a way.

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