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

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.