English

On the equiaffine symmetric hyperspheres

Differential Geometry 2014-08-20 v1

Abstract

We introduce and study the equiaffine symmetric {\bf hyperspheres}. For the first step we consider the locally strongly convex ones. In fact, by the idea used by Naitoh, we provide in this paper a direct proof of the complete classification for those affine symmetric hyperspheres. Then, via an earlier result of the first author, we are able to provide an alternative proof for the classification theorem of the affine hypersurface with parallel Fubini-Pick forms, which has already been established by Z.J. Hu et al in a totally different way.

Keywords

Cite

@article{arxiv.1408.4317,
  title  = {On the equiaffine symmetric hyperspheres},
  author = {Xingxiao Li and Guosong Zhao},
  journal= {arXiv preprint arXiv:1408.4317},
  year   = {2014}
}

Comments

19 pages, already submitted in May, 2014. arXiv admin note: substantial text overlap with arXiv:1303.4278, arXiv:1401.0860