Darboux-Weinstein theorem for locally conformally symplectic manifolds

TL;DR

This paper extends the Darboux-Weinstein theorem to locally conformally symplectic manifolds, providing a local normal form result and applications to Lagrangian submanifolds.

Contribution

It introduces a Darboux-Weinstein type theorem for LCS manifolds, a significant generalization of classical symplectic results.

Findings

Established a local normal form theorem for LCS manifolds.

Applied the theorem to study Lagrangian submanifolds in LCS geometry.

Provided new tools for analyzing the structure of LCS manifolds.

Abstract

A locally conformally symplectic (LCS) form is an almost symplectic form $\omega$ such that a closed one-form $\theta$ exists with $d\omega = \theta \wedge \omega$. We present a version of the well-known result of Darboux and Weinstein in the LCS setting and give an application concerning Lagrangian submanifolds.