Para-Ricci-like Solitons with Vertical Potential on Para-Sasaki-like Riemannian π-Manifolds

The objects of study are para-Ricci-like solitons on para-Sasaki-like, almost paracontact, almost paracomplex Riemannian manifolds, namely, Riemannian pi-manifolds. Different cases when the potential of the soliton is the Reeb vector field or pointwise collinear to it are considered. Some additional geometric properties of the constructed objects are proven. Results for a parallel symmetric second-order covariant tensor on the considered manifolds are obtained. An explicit example of dimension 5 in support of the given assertions is provided.

Automated summary

The study focuses on para-Ricci-like solitons on certain types of Riemannian manifolds, considering different scenarios related to the soliton potential. By proving additional geometric properties and obtaining results related to parallel symmetric second-order covariant tensor on the manifolds, support is provided for the given assertions. An explicit example in dimension 5 is presented to illustrate the findings.