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CR submanifolds in a sphere and their Gauss maps

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Abstract

The relationship between CR submanifolds in a sphere and their Gauss maps are investigated. Let V be the image of a sphere by a rational holomorphic map F with degree two in another sphere. It is show that the Gauss map of V is degenerate if and only if F is linear fractional.

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Authors and Affiliations

  1. Department of Mathematics, Jilin Normal University, Siping, 136000, China

    XiaoLiang Cheng

  2. Department of Mathematics, Capital Normal University, Beijing, 100048, China

    XiaoLiang Cheng

  3. Department of Mathematics, University of Houston, Houston, TX, 77204, USA

    ShanYu Ji

  4. Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing, 102617, China

    WeiMing Liu

Authors
  1. XiaoLiang Cheng
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  2. ShanYu Ji
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  3. WeiMing Liu
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Correspondence to ShanYu Ji.

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Cheng, X., Ji, S. & Liu, W. CR submanifolds in a sphere and their Gauss maps. Sci. China Math. 56, 1041–1049 (2013). https://doi.org/10.1007/s11425-013-4597-x

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  • DOI: https://doi.org/10.1007/s11425-013-4597-x

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