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Spring 2002 A convexity theorem for torus actions on contact manifolds
Eugene Lerman
Illinois J. Math. 46(1): 171-184 (Spring 2002). DOI: 10.1215/ijm/1258136148


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.


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Eugene Lerman. "A convexity theorem for torus actions on contact manifolds." Illinois J. Math. 46 (1) 171 - 184, Spring 2002.


Published: Spring 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1021.53061
MathSciNet: MR1936083
Digital Object Identifier: 10.1215/ijm/1258136148

Primary: 53D20
Secondary: 37J05 , 37J15 , 53D10

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign


Vol.46 • No. 1 • Spring 2002
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