Skip to main content
Log in

Regular space-like hypersurfaces in S m+11 with parallel para-Blaschke tensors

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

Abstract

In this paper, we give a complete conformal classification of the regular space-like hypersurfaces in the de Sitter Space Sm+1 1 with parallel para-Blaschke tensors.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cheng, Q. M., Li, X. X., Qi, X. R.: A classification of hypersurfaces with parallel para-Blaschke tensor in Sm+1. Internat. J. Math., 21, 297–316 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hertrich-Jeromin, U.: Introduction to Möbius differential geometry, vol.300 of London Mathematical Society, Lecture Note Series, Cambridge University Press, Cambridge, 2003

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Hu, Z. J., Li, X. X., Zhai, S. J.: On the Blaschke isoparametric hypersurfaces in the unit sphere with three distinct Blaschke eigenvalues. Sci. China Ser. A, 54, 2171–2194 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Li, H. Z., Wang, C. P.: Möbius geometry of hypersurfaces with constant mean curvature and scalar curvature. Manuscripta Math., 112, 1–13 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Li, T. Z., Ma, X., Wang, C. P.: Möbius homogeneous hypersurfaces with two distinct principal curvatures in Sn+1. Ark. Mat., 51, 315–328 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Li, T. Z., Wang, C. P.: A note on Blaschke isoparametric hypersurfaces. Internat. J. Math., 25(12), 1450117 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Li, T. Z., Qing, J., Wang, C. P.: Möbius curvature, Laguerre curvature and Dupin hypersurface. Adv. Math., 311, 249–294 (2017)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. Li, X. X., Zhang, F. Y.: Immersed hypersurfaces in the unit sphere Sm+1 with constant Blaschke eigenvalues. Acta Math. Sin., Engl. Ser., 23(3), 533–548 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, X. X., Song, H. R.: On the regular space-like hypersurfaces with parallel Blaschke tensors in the de Sitter space Sm+1 1. J. of Math. (PRC), 36(6), 1183–1200 (2016)

    MATH  Google Scholar 

  12. Lin, L. M., Guo, Z.: Classification of hypersurfaces with two distinct principal curvatures and closed Möbius form in Sm+1. Sci. China Ser. A, 55(7), 1463–1478 (2012)

    Article  MATH  Google Scholar 

  13. Nie, C. X., Wu, C. X.: Space-like hypersurfaces with parallel conformal second fundamental forms in the conformal space. Acta Math. Sinica, Chin. Ser., 51(4), 685–692 (2008)

    MathSciNet  MATH  Google Scholar 

  14. 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 

  15. Nie, C. X.: The space-like surfaces with vanishing conformal form in the conformal space. arXiv [math.DG]: 1108.2943v1, 15 Aug, 2011

    MATH  Google Scholar 

  16. Nie, C. X., Wu, C. X.: Regular submanifolds in the conformal space Qn p. Chin. Ann. Math., 33, 695–714 (2012)

    Article  MATH  Google Scholar 

  17. Nie, C. X., Li, T. Z.: Conformal geometry of hypersurfaces in Lorentz space forms. Geometry, 2013, Article ID 549602, http://dx.doi.org/10.1155/2013/549602

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  19. Zhong, D. X., Sun, H. A.: On hypersurfaces in the unit sphere with constant para-Blaschke eigenvalues. Acta Math. Sinica, Chin. Ser., 51(3), 579–592 (2008)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors are grateful for the referee’s valuable and helpful comments on the first version.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hong Ru Song.

Additional information

Supported by Foundation of Natural Sciences of China (Grant Nos. 11671121, 11171091 and 11371018)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, X.X., Song, H.R. Regular space-like hypersurfaces in S m+11 with parallel para-Blaschke tensors. Acta. Math. Sin.-English Ser. 33, 1361–1381 (2017). https://doi.org/10.1007/s10114-017-6208-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-017-6208-1

Keywords

MR(2010) Subject Classification

Navigation