On CR (Cauchy-Riemann) almost cosymplectic manifolds

TL;DR

This paper develops a CR geometric framework for studying almost cosymplectic manifolds with Kahlerian leaves, providing local descriptions and introducing a canonical Hermitian complex connection.

Contribution

It introduces a CR geometric approach to analyze almost cosymplectic manifolds and defines a canonical Hermitian complex connection within this context.

Findings

Local description of almost cosymplectic structures in mixed coordinates

Introduction of a canonical Hermitian complex connection

Detailed analysis of almost cosymplectic (-1,μ,0)-spaces

Abstract

In the paper we develop a framework for the alternative way of the study of a local geometry of almost cosymplectic manifolds with Kahlerian leaves. The main idea is to apply the concept of a geometry and analysis of CR manifolds. Locally the almost cosymplectic manifold is modeled on the 'mixed' space RxCn. There is given a complete local description of the underlying almost contact metric structure in the system of local, mixed - real, complex- coordinates. We also introduce a notion of a canonical Hermitian complex connection in the CR structure of a CR almost cosymplectic manifold. As an example we provide detailed descritpion of almost cosymplectic $(-1,\mu,0)$-spaces.