Mikami-Weinstein Type Theorem for Cosymplectic Groupoid Actions

TL;DR

This paper extends the Mikami-Weinstein theorem to cosymplectic groupoid actions, providing a new reduction framework for cosymplectic manifolds in the context of groupoid symmetries.

Contribution

It introduces the concept of cosymplectic groupoid actions and proves an analogue of the Mikami-Weinstein theorem for these actions.

Findings

Established a cosymplectic groupoid action framework.

Proved a Mikami-Weinstein type reduction theorem for cosymplectic manifolds.

Provided foundational results for future studies in cosymplectic geometry.

Abstract

The Mikami-Weinstein theorem is a generalization of the classical Marsden-Weinstein-Meyer symplectic reduction theorem to the case of symplectic groupoid actions. In this paper, we introduce the notion of a cosymplectic groupoid action on a cosymplectic manifold and prove a theorem which is a natural analogue of the Mikami-Weinstein theorem.