Locally conformally symplectic reduction

TL;DR

This paper introduces a reduction method for locally conformally symplectic manifolds with group actions, extending to locally conformally Kähler and contact structures, broadening geometric reduction techniques.

Contribution

It develops a new reduction procedure for LCS manifolds with symmetry, compatible with LCK and contact structures, enhancing geometric analysis tools.

Findings

Reduction procedure for LCS manifolds with group actions

Compatibility with LCK structures under certain conditions

Contact reduction as a special case

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 K\"ahler structure. As a special consequence, we obtain a compatible contact reduction with respect to any regular value of the contact momentum mapping.