Moment maps on symplectic cones

Suzana Falcão B. de Moraes and Carlos Tomei

Vol. 181 (1997), No. 2, 357–375

DOI: 10.2140/pjm.1997.181.357

Abstract

We analyze some convexity properties of the image maps on symplectic cones, similar to the ones obtained by Guillemin-Sternberg and Atiyah for compact symplectic manifolds in the early 80’s. We prove the image of the moment map associated to the symplectic action of an n-torus on a symplectic cone is a polytopic convex cone in Rⁿ. Then, we generalize these results to symplectic manifolds obtained by special perturbations of the symplectic structure of a cone: we obtain sufficient (and essentially necessary) conditions for the image of the moment map associated to the perturbed form to remain unchanged.

Milestones

Received: 20 May 1993

Revised: 17 November 1996

Published: 1 December 1997