A convexity theorem for torus actions on contact manifolds

Details A convexity theorem for torus actions on contact manifolds A convexity theorem for torus actions on contact manifolds

2000-12-04

arxiv.org/abs/math/0012017v2

Mathematics

Symplectic Geometry

10 pages. v2: minor changes, two references added

Scientific paper

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.

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