Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure

We introduce and study a new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure corresponding to an almost paracomplex structure. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field were considered. It was proved a necessary and sufficient condition for the manifold to admit a para-Ricci-like soliton, which is the structure that is para-Einstein-like. Explicit examples are provided in support of the proven statements.

Automated summary

A new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure has been introduced and studied. Special cases such as para-Einstein-like, para-Sasaki-like, and having a torse-forming Reeb vector field were considered. A necessary and sufficient condition for the manifold to admit a para-Ricci-like soliton, similar to para-Einstein, was proven, with explicit examples provided in support.