Skip to main content
SpringerLink
Log in

Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

The conformal geometry of regular hypersurfaces in the conformal space is studied. We classify all the conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in the conformal space up to conformal equivalence.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hu Z J, Li H Z. Classification of hypersurfaces with parallel Möbius second fundamental form in Sn+1. SciChina Ser A, 2004, 47: 417–430

    Article  MATH  MathSciNet  Google Scholar 

  2. Li H Z, Liu H L, Wang C P, et al. Möbius isoparametric hypersurfaces in Sn+1 with two distinct principal curvatures. Acta Math Sinica Engl Ser, 2002, 18: 437–446

    Article  MATH  MathSciNet  Google Scholar 

  3. Li Z Q, Xie Z H. Space-like isoparametric hypersurfaces in Lorentzian space forms. Front Math China, 2006, 1: 130–137

    Article  MathSciNet  Google Scholar 

  4. Magid M A. Lorentzian isoparametric hypersurface. Pacific J Math, 1985, 118: 437–446

    MathSciNet  Google Scholar 

  5. Nie C X. Conformal geometry of hypersurfaces and surfaces in Lorentzian space forms (in Chinese). Dissertation for the Doctoral Degree. Beijing: Peking University, 2006, 17–27, 41–52

    Google Scholar 

  6. Nie C X, Ma X, Wang C P. Conformal CMC-surfaces in Lorentzian space forms. Chin Ann Math Ser B, 2007, 28: 299–310

    Article  MATH  MathSciNet  Google Scholar 

  7. Nie C X, Wu C X. Regular submanifolds in conformal spaces (in Chinese). Chin Ann Math Ser A, 2008, 29: 315–324

    MATH  MathSciNet  Google Scholar 

  8. Nie C X, Wu C X. Space-like hyperspaces with parallel conformal second fundamental forms in the conformal space (in Chinese). Acta Math Sinica Chin Ser, 2008, 51: 685–692

    Article  MATH  MathSciNet  Google Scholar 

  9. Nomizu K. On isoparametric hypersurfaces in the Lorentzian space forms. Japan J Math, 1981, 7: 217–216

    MATH  MathSciNet  Google Scholar 

  10. Xiao L. Lorentzian isoparametric hypersurfaces in H n+11 . Pacific J Math, 1999, 189: 377–397

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Sciences, Hubei University, Wuhan, 430062, China

    ChangXiong Nie

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    ChangXiong Nie

  3. Faculty of Sciences, Beijing Institute of Technology, Beijing, 100081, China

    TongZhu Li

  4. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China

    YiJun He

  5. Institute of Mathematics, Hubei University, Wuhan, 430062, China

    ChuanXi Wu

Authors
  1. ChangXiong Nie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. TongZhu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. YiJun He
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. ChuanXi Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to ChangXiong Nie.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nie, C., Li, T., He, Y. et al. Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space. Sci. China Math. 53, 953–965 (2010). https://doi.org/10.1007/s11425-009-0206-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-009-0206-4

Keywords

MSC(2000)

Search

Navigation