A convexity theorem for torus actions on contact manifolds
Symplectic Geometry
2007-05-23 v2 Differential Geometry
Abstract
We show that the cone associated with 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.
Cite
@article{arxiv.math/0012017,
title = {A convexity theorem for torus actions on contact manifolds},
author = {Eugene Lerman},
journal= {arXiv preprint arXiv:math/0012017},
year = {2007}
}
Comments
10 pages. v2: minor changes, two references added