Skip to main content
Log in

The jacobi equation on naturally reductive compact Riemannian homogeneous spaces

  • Published:
Commentarii Mathematici Helvetici

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.

References

  1. Berger, M., Les variétés riemanniennes homogènes normales simplement connexes à courbure strictement positive,Ann. Scoula Norm. Sup. Pisa, 15 (1961), 179–246.

    MATH  Google Scholar 

  2. Bott, R., Samelson, H., Applications of Morse theory to symmetric spaces,Amer. J. of Math., 80 (1958), 964–1029.

    Article  MathSciNet  Google Scholar 

  3. Chavel, I., A class of riemannian homogeneous spaces,J. of Diff. Geom., 4 (1970), 13–20.

    MATH  MathSciNet  Google Scholar 

  4. Chavel, I., On normal riemannian homogeneous spaces of rank 1,Bull. Amer. Math. Soc., 73 (1967), 477–481.

    Article  MATH  MathSciNet  Google Scholar 

  5. Chavel, I., Isotropic Jacobi fields and Jacobi's equation on riemannian homogeneous spaces,Comm. Math. Helv., 42 (1967), 237–248.

    Article  MATH  MathSciNet  Google Scholar 

  6. Jensen, G. R., Einstein metrics on principal fibre bundles,J. Diff. Geom., 8 (1973), 599–614.

    MATH  Google Scholar 

  7. Kobayashi, S., Nomizu, K.,Foundations of Differential Geometry II, New York, Interscience, 1969.

    MATH  Google Scholar 

  8. Lukesh, G. W., Variations of metrics on homogeneous manifolds, preprint, University of Massachusetts, 1976.

  9. Rauch, H. E., Geodesics and Jacobi equations on homogeneous riemannian manifolds,Proc. U.S. Japan Seminar in Differential Geometry, (Kyoto Univ., 1965), 115–127.

  10. Ziller, W., Closed geodesics on homogeneous spaces, to appear inMath Z.

  11. Ziller, W., The free-loop space of globally symmetric spaces, preprint, Bonn, 1975.

  12. Weinstein, A., Distance spheres in complex projective spaces,Proc. Am. Math. Soc., 39 (1973).

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was supported by the “Sonderforschungsbereich Theoretische Mathematik (SFB 40)” at the University of Bonn and completed at the Institute for Advanced Study with partial support from a National Science Foundation grant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ziller, W. The jacobi equation on naturally reductive compact Riemannian homogeneous spaces. Commentarii Mathematici Helvetici 52, 573–590 (1977). https://doi.org/10.1007/BF02567391

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02567391

Keywords

Navigation