Annals of Global Analysis and Geometry

, Volume 11, Issue 2, pp 165-171

First online:

Some remarks on R-contact flows

  • Philippe RukimbiraAffiliated withDepartment of Mathematics, Florida International University

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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