Gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian $\Pi$-manifolds

TL;DR

This paper investigates gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian $\

Contribution

It proves that these solitons have constant coefficients and scalar curvatures, providing explicit examples and detailed geometric properties.

Findings

Soliton coefficients are constant.

Scalar curvatures are equal and constant.

Ricci tensor is proportional to the vertical component.

Abstract

Gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian $\Pi$-manifolds are studied. It is proved that these objects have constant soliton coefficients. For the soliton under study is shown that the corresponding scalar curvatures of the considered both metrics are equal and constant and its Ricci tensor is a constant multiple of the vertical component. Explicit example of a 3-dimensional para-Sasaki-like Riemannian $\Pi$-manifold is provided in support of the proved assertions.