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

Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $\mathrm{\Pi }$-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.