Illinois Journal of Mathematics

A convexity theorem for torus actions on contact manifolds

Eugene Lerman

Full-text: Open access


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.

Article information

Illinois J. Math., Volume 46, Number 1 (2002), 171-184.

First available in Project Euclid: 13 November 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D20: Momentum maps; symplectic reduction
Secondary: 37J05: General theory, relations with symplectic geometry and topology 37J15: Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20] 53D10: Contact manifolds, general


Lerman, Eugene. A convexity theorem for torus actions on contact manifolds. Illinois J. Math. 46 (2002), no. 1, 171--184. doi:10.1215/ijm/1258136148.

Export citation