2018/04/04 by Szancer, Zuzanna
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1804.01599
In this paper we study \widetildeJ-tangent affine hyperspheres, where \widetildeJ is the canonical para-complex structure on ℝ2n+2. The main purpose of this paper is to give a classification of \widetildeJ-tangent affine hyperspheres of an arbitrary dimension with an involutive distribution D. In particular, we classify all such hyperspheres in the 3-dimensional case. We also show that there is a direct relation between \widetildeJ-tangent affine hyperspheres and Calabi products. As an application we obtain certain classification results. In particular, we show that, with one exception, all odd dimensional proper flat affine hyperspheres are, after a suitable affine transformation, \widetildeJ-tangent. Some examples of \widetildeJ-tangent affine hyperspheres are also given.