Archiv der Mathematik

, Volume 68, Issue 1, pp 65–69 | Cite as

A fixed point theorem

  • Fabio Podestà


We establish a fixed point theorem for a Lie group of isometries acting on a Riemannian manifold with nonnegative curvature.

Mathematics Subject Classification (1991)

53C12 53C30 58C30 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. V. Alekseevsky, Riemannian manifolds of cohomogeneity one. Colloq. Math. Soc. János Bolyai 56, 9–22(1989).MathSciNetGoogle Scholar
  2. [2]
    A. V. Alekseevsky and D. V. Alekseevsky, Asystatic G-manifolds. Preprint, Vienna 1993.Google Scholar
  3. [3]
    A. Besse, Einstein manifolds. Berlin-Heidelberg-New York 1986.Google Scholar
  4. [4]
    G. E. Bredon, Introduction to compact transformation groups. New York-London 1972.Google Scholar
  5. [5]
    W. Hsiang and H. B. Lawson, Minimal submanifolds of low cohomogeneity. J. Differential Geom. 5, 1–38 (1971).MATHMathSciNetGoogle Scholar
  6. [6]
    H. Kim and P. Tondeur, Riemannian foliations on manifolds with non-negative curvature. Manuscripta Math. 74, 39–45 (1992).MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    S. Kobayashi, Transformations groups in differential geometry. Ergeb. Math. Grenzgeb. 70, Berlin-Heidelberg-New York 1972.Google Scholar
  8. [8]
    F. Podestà, Immersion of cohomogeneity one Riemannian manifolds. Preprint 1994.Google Scholar
  9. [9]
    B. L. Reinhart, Foliated manifolds with bundle-like metrics. Ann. of Math. 69,119–132 (1959).CrossRefMathSciNetGoogle Scholar
  10. [10]
    T. Takahashi, Minimal immersions of Riemannian manifolds. J. Math. Soc. Japan 18, 380–385 (1966).MATHMathSciNetCrossRefGoogle Scholar
  11. [11]
    G. Walschap, Metric foliations and curvature. J. Geom. Anal. 2, 373–381 (1992).MATHMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Fabio Podestà
    • 1
  1. 1.Dept. of MathematicsUniversity of ParmaParmaItaly

Personalised recommendations