Locally conformally symplectic reduction

2018/08/31 by Stanciu, Miron
#53D05 #53D10 #53D20 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1809.00034

Abstract

We present a reduction procedure for locally conformally symplectic (LCS) manifolds with an action of a Lie group preserving the conformal structure, with respect to any regular value of the momentum mapping. Under certain conditions, this reduction is compatible with the existence of a locally conformally Kähler structure. As a special consequence, we obtain a compatible contact reduction with respect to any regular value of the contact momentum mapping.

Related

• Locally conformally symplectic reduction of the cotangent bundle
• Locally conformally symplectic bundles
• Interplay between Quantitative Aspects of Locally Conformally Symplectic Geometry and Contact Dynamics
• Parallelism between locally conformal symplectic manifolds and contact manifolds
• Darboux-Weinstein theorem for locally conformally symplectic manifolds