On the moment map on symplectic manifolds

2006/05/10 by Biliotti, Leonardo
#53C55 #57S15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0605270

Abstract

We consider a connected symplectic manifold M acted on by a connected Lie group G in a Hamiltonian fashion. If G is compact, we prove give an Equivalence Theorem for the symplectic manifolds whose squared moment map ∥ μ∥² is constant. This result works also in the almost-Kähler setting. Then we study the case when G is a non compact Lie group acting properly on M and we prove a splitting results for symplectic manifolds.

Related

• A note on the moment map on compact Kähler manifolds
• On Generalized Moment Maps for Symplectic Compact Group Actions
• Lie Group Valued Moment Maps
• The fundamental group of symplectic manifolds with Hamiltonian SU(2) or SO(3) actions
• Restriction of the moment map to certain non-Lagrangian submanifolds