Five dimensional almost para-cosymplectic manifolds with contact Ricci potential

TL;DR

This paper classifies 5-dimensional pseudo-Riemannian manifolds with almost para-cosymplectic structures, focusing on contact Ricci potential, flatness, and Lie group structures, expanding understanding of their geometric properties.

Contribution

It provides new classifications and descriptions of 5D almost para-cosymplectic manifolds with contact Ricci potential, including Lie group characterizations and flatness conditions.

Findings

Classified manifolds with contact Ricci potential

Described all simply connected Lie groups with invariant structures

Identified conditions for local flatness

Abstract

There are studied in details 5-dimensional pseudo-Riemannian manifolds equipped with the structure analogous to the almost cosymplectic (almost coKaehler) structure. The curvature by assumption commutes with the structure affinor and all these manifolds are Walker spaces. There are obtained classifications for manifolds for contact Ricci potential, locally flat manifolds and described all connected, simply connected Lie groups admiting left-invariant structure. There are some other more general results.