Skip to main content
SpringerLink
Log in

Homogeneous manifolds with nonpositive curvature operator

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

Homgeneous manifolds of nonpositive sectional curvature can be identified with a certain class of solvable Lie groups. We determine, which of these groups also admit metrics with nonpositive curvature operator; this class is smaller, but still contains many examples.

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. Azencott, R. and Wilson, E. ‘Homegeneous manifolds with negative curvature I’, Trans. Amer. Math. Soc. 215 (1976), 323–362.

    Google Scholar 

  2. Azencott, R. and Wilson, E. ‘Homogeneous manifolds with negative curvature II’, Mem. Amer. Math. Soc. 178 (1976).

  3. D'Atri, J. E. and Dotti, Miatello, I. ‘Eigenvalues of the curvature operator for certain homogeneous manifolds’ (preprint, 1989).

  4. Heintze, E. ‘On homogeneous manifolds of negative curvature’, Math. Ann. 211 (1974), 23–34.

    Google Scholar 

  5. Kobayashi, S. and Nomizu, K. Foundations of Differential Geometry, Vol. II, Interscience, New York, 1969.

    Google Scholar 

  6. Micaleff, M. and Moore, J. ‘Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes’, Ann. Of Math. 127 (1988), 199–227.

    Google Scholar 

  7. Sagle, A. and Walde, R. Introduction to Lie Groups and Lie Algebras, Academic Press, New York, 1973.

    Google Scholar 

  8. Simons, J. ‘On transitivity of holonomy systems’, Ann. of Math. 76 (1962), 213–234.

    Google Scholar 

  9. Tachibana, S. ‘A theorem on Riemannian manifolds of positive curvature operator’, Proc. Japan Acad. Ser. A 50 (1974), 301–302.

    Google Scholar 

  10. Wolf, J. ‘Homogeneity and bounded isometries in manifolds of negative curvature’, Illinois J. Math. 8 (1964), 14–18.

    Google Scholar 

  11. Wolter, T. ‘Homogene Mannigfaltigkeiten nichtpositiver Krümmung’, Thesis, Univ. Zürich, 1989.

  12. Wolter, T. ‘Einstein metrics on solvable groups’ (to appear).

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Zürich, Rämistrasse 74, CH-8001, Zürich, Switzerland

    Thomas H. Wolter

Authors
  1. Thomas H. Wolter
    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

Wolter, T.H. Homogeneous manifolds with nonpositive curvature operator. Geom Dedicata 37, 361–370 (1991). https://doi.org/10.1007/BF00181413

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00181413

Keywords

Search

Navigation