Abstract
We show that the image cone of a moment map for an action of a torus on a contact compact connected manifold is a convex polyhedral cone and that the moment map has connected fibers provided the dimension of the torus is bigger than 2 and that no orbit is tangent to the contact distribution. This may be considered as a version of the Atiyah-Guillemin-Sternberg convexity theorem for torus actions on symplectic cones and as a direct generalization of the convexity theorem of Banyaga and Molino for completely integrable torus actions on contact manifolds.
Citation
Eugene Lerman. "A convexity theorem for torus actions on contact manifolds." Illinois J. Math. 46 (1) 171 - 184, Spring 2002. https://doi.org/10.1215/ijm/1258136148
Information