Generalized almost para-contact manifolds

TL;DR

This paper introduces generalized almost para-contact manifolds, explores their properties, and relates them to classical structures, revealing new geometric frameworks with potential applications in differential geometry.

Contribution

It presents the concept of generalized almost para-contact manifolds, establishes normality conditions, and links them to Lie bialgebroid structures, expanding the understanding of para-contact geometry.

Findings

Generalized almost para-contact manifolds are introduced and characterized.

Normality conditions are expressed via classical tensor fields.

Connections to Lie bialgebroid and quasi-Lie algebroid structures are established.

Abstract

In this paper, we introduce generalized almost para-contact manifolds and obtain normality conditions in terms of classical tensor fields. We show that such manifolds naturally carry certain Lie bialgebroid/quasi-Lie algebroid structures on them and we relate this new generalized manifolds with classical almost para-contact manifolds. The paper contains several examples.