2014/08/19 by Xingxiao Li, Li, Xingxiao, Guosong Zhao +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #math.DG
paper · pdf · doi:10.48550/arxiv.1408.4317
19 pages, already submitted in May, 2014. arXiv admin note: substantial text overlap with arXiv:1303.4278, arXiv:1401.0860
arxiv created 2014/08/19 · arxiv updated 2014/08/20
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.