Skip to main content
Log in

Blaschke isoparametric hypersurfaces in the conformal space ℚ n+11 , I

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

Let x: M → Q n+11 be a regular hypersurface in the conformal space Q n+11 . We classify all the space-like Blaschke isoparametric hypersurfaces with two distinct Blaschke eigenvalues in the conformal space up to the conformal equivalence.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Li, H. Z., Liu, H. L., Wang, C. P., et al.: Moebius isoparametric hypersurfaces in Sn+1 with two distinct principal curvatures. Acta Math. Sin., Engl. Series, 18, 437–446 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Li, X. X., Peng, Y. J.: Classification of the Blaschke isoparametric hypersurfaces with three distinct Blaschke eigenvalues. Result. Math., 58, 145–172 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Li, X. X., Zhang, F. Y.: A Möbius classification of immersed hypersurfaces in spheres with parallel Blaschke tensors. Tohoku J. Math., 58, 581–597 (2006)

    Article  MATH  Google Scholar 

  4. Li, X. X., Zhang, F. Y.: Immersed hypersurfaces in the unit sphere Sm+1 with constant Blaschke eigenvalues. Acta Math. Sin., Engl. Series, 23, 533–548 (2007)

    Article  MATH  Google Scholar 

  5. Li, X. X., Zhang, F. Y.: On the Blaschke isoparametric hypersurfaces in the unit sphere. Acta Math. Sin., Engl. Series, 25, 657–678 (2009)

    Article  MATH  Google Scholar 

  6. Nie, C. X., Li, T. Z., He, Y. J., et al.: Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space. Sci. China Ser. A, 53(4), 953–965 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Nie, C. X., Wu, C. X.: Classification of type I time-like hyperspaces with parallel conformal second fundamental forms in the conformal space (in Chinese). Acta Math. Sin., Chin. Series, 54, 125–136 (2011)

    MathSciNet  MATH  Google Scholar 

  8. Nie, C. X., Wu, C. X.: Regular Submanifolds in the Conformal Space Qnp. Chin. Ann. Math., 33B, 695–714 (2012)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. Wang, C. P.: Moebius geometry of submanifolds in Sn. Manuscripta Math., 96, 517–534 (1998)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to ChanG Xiong Nie.

Additional information

Supported by China Scholarship Council (Grant No. [2011]5025)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nie, C.X. Blaschke isoparametric hypersurfaces in the conformal space ℚ n+11 , I. Acta. Math. Sin.-English Ser. 31, 1751–1758 (2015). https://doi.org/10.1007/s10114-015-4077-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-015-4077-z

Keywords

MR(2010) Subject Classification

Navigation