Commuting Pairs of Generalized Contact Metric Structures

TL;DR

This paper establishes a criterion for generating commuting pairs of generalized almost complex structures on product spaces of generalized contact metric spaces, impacting the understanding of generalized Sasakian and coKähler geometries.

Contribution

It introduces a new theorem providing a simple criterion for commuting structures, advancing the theoretical framework of generalized contact and complex geometries.

Findings

Provides a criterion for commuting generalized structures

Links to generalized Sasakian and coKähler geometries

Enhances understanding of product spaces in generalized geometry

Abstract

In this paper, we prove a theorem that gives a simple criterion for generating commuting pairs of generalized almost complex structures on spaces that are the product of two generalized almost contact metric spaces. We examine the implications of this theorem with regard to the definition of generalized Sasakian and generalized coK\"ahler geometry.