Annals of Global Analysis and Geometry

, Volume 11, Issue 2, pp 165–171

Some remarks on R-contact flows

  • Philippe Rukimbira


Let (M, α) be an R-contact manifold, then the set of periodic points of the characteristic vector field is a nonempty union of closed, totally geodesic odd-dimensional submanifolds. Moreover, the R-metric cannot have nonpositive sectional curvature. We also prove that no R-contact form can exist on any torus.

Key words

R-contact nonpositive sectional curvature harmonic forms 

MSC 1991

58 F 22 58 F 18 53 C 15 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Banyaga, A.; Rukimbira, P.:On R-contact manifolds. Preprint.Google Scholar
  2. [2]
    Banyaga, A.; Fathi A.; Rukimbira, P.: On characteristics of R-contact manifolds. In preparation.Google Scholar
  3. [3]
    Blair, D.:Contact manifolds in Riemannian Geometry. Lect. Notes in Math.509, Springer Verlag.Google Scholar
  4. [4]
    Carrière, Y.: Flots riemanniens. InStructures Transerves des Feuilletages. Astérisque 116 (1982), 31–52.Google Scholar
  5. [5]
    Kobayashi, S.: Fixed points of isometries.Nagoya Math. J. 13 (1958), 63–68.Google Scholar
  6. [6]
    Lutz, R.: Sur la géometrie des structures de contact invariantes.Ann. Inst. Fourier (Grenoble)29 (1979), 283–306.Google Scholar
  7. [7]
    Lawson, H.B.;Yau, S.T.: Compact manifolds of nonpositive curvature.J. Differential Geom. 7 (1972), 211–228.Google Scholar
  8. [8]
    Poor, W.:Differential Geometric Structures. McGraw-Hill Book Company, 1981.Google Scholar
  9. [9]
    Reinhart, B.: Foliated manifolds with bundle-like metrics.Ann. of Math. 69 (1959), 119–132.Google Scholar
  10. [10]
    Rukimbira, P.:Some properties of almost contact flows. Ph. D. Thesis, Penn Stàte University, 1991.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Philippe Rukimbira
    • 1
  1. 1.Department of MathematicsFlorida International UniversityMiamiUSA

Personalised recommendations