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On the Equiaffine Symmetric Hyperspheres

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Abstract

We introduce and study the equiaffine symmetric hyperspheres. For the first step we consider the locally strongly convex ones. In fact, by the idea used by H. 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.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Henan Normal University, Xinxiang, 453007, Henan, People’s Republic of China

    Xingxiao Li

  2. School of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Guosong Zhao

Authors
  1. Xingxiao Li
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  2. Guosong Zhao
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Correspondence to Xingxiao Li.

Additional information

Research supported by NSFC (Nos. 11171091, 11371018) and partially supported by NSF of Henan Province (No. 132300410141).

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Li, X., Zhao, G. On the Equiaffine Symmetric Hyperspheres. Results. Math. 68, 117–142 (2015). https://doi.org/10.1007/s00025-014-0426-y

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  • DOI: https://doi.org/10.1007/s00025-014-0426-y

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