Para-Ricci-like Solitons on Almost Paracontact Almost Paracomplex Riemannian Manifolds

TL;DR

This paper introduces and analyzes para-Ricci-like solitons on a special class of geometric manifolds, establishing conditions for their existence and providing explicit examples.

Contribution

It defines para-Ricci-like solitons on almost paracontact almost paracomplex Riemannian manifolds and characterizes when these manifolds are para-Einstein-like.

Findings

Necessary and sufficient conditions for para-Ricci-like solitons

Characterization of special cases like para-Sasaki-like

Explicit examples illustrating the theory

Abstract

It is introduced and studied para-Ricci-like solitons with potential Reeb vector field on almost paracontact almost paracomplex Riemannian manifolds. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field have been considered. It is proved a necessary and sufficient condition the manifold to admit a para-Ricci-like soliton which is the structure to be para-Einstein-like. Explicit examples are provided in support of the proven statements.