A convexity theorem for torus actions on contact manifolds

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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.

Original languageEnglish (US)
Pages (from-to)171-184
Number of pages14
JournalIllinois Journal of Mathematics
Issue number1
StatePublished - 2002

ASJC Scopus subject areas

  • Mathematics(all)


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