Rukimbira, P. Ann Glob Anal Geom (1993) 11: 165. doi:10.1007/BF00773454
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.
R-contactnonpositive sectional curvatureharmonic forms