Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $\Pi$-manifolds

TL;DR

This paper introduces and analyzes para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian -manifolds, revealing their Ricci tensor properties and providing an explicit Lie group example.

Contribution

It is the first to study para-Ricci-like solitons with arbitrary potential on para-Sasaki-like -manifolds, establishing key properties and an explicit example.

Findings

Ricci tensor is a constant multiple of the vertical metric component

Scalar curvatures of both metrics are equal and constant

Explicit Lie group example provided

Abstract

Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $\Pi$-manifolds are introduced and studied. For the studied soliton, it is proved that its Ricci tensor is a constant multiple of the vertical component of both metrics. Thus, the corresponding scalar curvatures of both considered metrics are equal and constant. An explicit example of the Lie group as the manifold under study is presented.