Ricci-like solitons on almost contact B-metric manifolds

TL;DR

This paper introduces and investigates Ricci-like solitons with Reeb vector field potential on almost contact B-metric manifolds, establishing conditions for their existence and providing explicit Lie group examples.

Contribution

It defines Ricci-like solitons in this context and proves their equivalence to Einstein-like structures in specific cases, with explicit examples.

Findings

Ricci-like solitons exist iff the structure is Einstein-like in Sasaki-like and torse-forming cases

Explicit 3- and 5-dimensional Lie group examples are constructed

Conditions for Ricci-like solitons are characterized on almost contact B-metric manifolds

Abstract

Ricci-like solitons with potential Reeb vector field are introduced and studied on almost contact B-metric manifolds. The cases of Sasaki-like manifolds and torse-forming potentials have been considered. In these cases, it is proved that the manifold admits a Ricci-like soliton if and only if the structure is Einstein-like. Explicit examples of Lie groups as 3- and 5-dimensional manifolds with the structures studied are provided.