Skip to main content
SpringerLink
Log in

Totally geodesic submanifolds in compact Riemannian symmetric spaces and their stability

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we determine a large class of totally geodesic submanifolds of a compact Riemannian symmetric space. The stability of these submanifolds in their ambient space is also determined.

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. Chen Bang-Yen, Nagano, T., Totally geodesic submanifolds of symmetric spaces II, Duke Math. J., 1978, 45: 405.

    Article  MATH  MathSciNet  Google Scholar 

  2. Nagano, T., The involutions of compact symmetric spaces, Tokyo J. Math., 1998, 11: 57.

    Article  MathSciNet  Google Scholar 

  3. Ohnita, Y., On the stability of minimal submanifolds in compact symmetric spaces, Composite Mathemetica, 1996, 64: 157.

    MathSciNet  Google Scholar 

  4. Sumi, M., On the stability of minial submanifolds in symmetric spaces, Tsukuba J. Math., 1995, 19: 27.

    MATH  MathSciNet  Google Scholar 

  5. Naitoh, H., Compact simple Lie algebras with two involutions and submanifolds of compact symmetric space I, II, Osaka J. Math., 1993, 30: 653.

    MATH  MathSciNet  Google Scholar 

  6. Yen, C., Sur les espace symetriques non compacts, Scientia Sinica, 1965, 14: 31.

    MATH  MathSciNet  Google Scholar 

  7. Kobayashi, S., Nomizu, K., Foundations of differential geometry, New York: Interscience Publishers, 1969.

    MATH  Google Scholar 

  8. Helgason, S., Differential geometry, Lie Groups and Symmetric Spaces, New York: Academic Press, 1978.

    MATH  Google Scholar 

  9. Goto, M. Kobayashi, E. T., On the subgroups of the centers of simply connected simple lie groups-Classification of simple Lie groups in the Large, Osaka, J.Math., 1969, 6: 151.

    MathSciNet  Google Scholar 

  10. Takeuchi, M., On fundamental group and the group of isometries of a symmetric spaces, J. Fac. Sci. Univ. Tokyo, Sect. 1, 1964, 10: 88.

    MATH  Google Scholar 

  11. Hsiang, W. Y., Hou Zixin, Meng Daoji, Lectures on Lie groups (in Chinese), Beijing: Peking University Press, 1992.

    Google Scholar 

  12. Mckay, W. G., Patera, J., Tables of dimensions, indices and branching rules for representations of simple Lie algebras, Lect. Notes in Pure and Appl. Math. 69, New York-Basel: Marcel-Dekker, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics,Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, Beijing, China

    Quanqin Jin

  2. Department of Mathematics, Hebei University, 071002, Baoding, China

    Quanqin Jin

Authors
  1. Quanqin Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jin, Q. Totally geodesic submanifolds in compact Riemannian symmetric spaces and their stability. Sci. China Ser. A-Math. 43, 1279–1293 (2000). https://doi.org/10.1007/BF02880065

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02880065

Keywords

Search

Navigation