Cosymplectic Lagrangian-like submanifolds

TL;DR

This paper explores the geometric properties of cosymplectic manifolds, focusing on Lagrangian submanifolds, compatible structures, and neighborhood theorems, drawing parallels with symplectic geometry.

Contribution

It introduces the study of Lagrangian Grassmannian and compatible structures in cosymplectic geometry, extending classical symplectic results to the cosymplectic setting.

Findings

Analysis of the Lagrangian Grassmannian in cosymplectic geometry

Introduction of compatible co-complex structures

Derivation of the Weinstein 1-form and its de Rham class

Abstract

This paper highlights the similarities between even-dimensional geometry (symplectic) and odd-dimensional geometry (cosymplectic). We study the Lagrangian Grassmannian in the cosymplectic setting. The space of compatible co-complex structures is introduced and analyzed. A study of Moser's trick and Lagrangian neighborhood theorems in the cosymplectic context follows. The corresponding Weinstein $1-$form is derived, and its de Rham class is a co-flux.