A convexity theorem for torus actions on contact manifolds
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- December 2000
- DOI:
- 10.48550/arXiv.math/0012017
- arXiv:
- arXiv:math/0012017
- Bibcode:
- 2000math.....12017L
- Keywords:
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- Symplectic Geometry;
- Differential Geometry
- E-Print:
- 10 pages. v2: minor changes, two references added