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Classification of hypersurfaces with parallel Möbius second fundamental form in S n+1

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Abstract

Let M n(n ≥ 2) be an immersed umbilic-free hypersurface in the (n+1)-dimensional unit sphere S n+1. Then M n is associated with a so-called Möbius metric g, and a Möbius second fundamental form B which are invariants of M nunder the Möbius transformation group of S n+1. In this paper, we classify all umbilic-free hypersurfaces with parallel Möbius second fundamental form.

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Authors and Affiliations

  1. Department of Mathematics, Zhengzhou University, 450052, Zhengzhou, China

    Hu Zejun

  2. Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China

    Li Haizhong

Authors
  1. Hu Zejun
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  2. Li Haizhong
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Correspondence to Hu Zejun or Li Haizhong.

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Hu, Z., Li, H. Classification of hypersurfaces with parallel Möbius second fundamental form in S n+1 . Sci. China Ser. A-Math. 47, 417–430 (2004). https://doi.org/10.1360/03ys0134

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  • DOI: https://doi.org/10.1360/03ys0134

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