Almost Ricci-like solitons with torse-forming vertical potential of constant length on almost contact B-metric manifolds

TL;DR

This paper explores a generalization of Ricci-like solitons with a specific potential on almost contact B-metric manifolds, establishing conditions for equivalence to Einstein-like metrics and providing explicit examples.

Contribution

It introduces a new class of Ricci-like solitons with torse-forming potentials and characterizes their properties and relations to Einstein-like metrics.

Findings

Conditions for equivalence to almost Einstein-like metrics

Results for parallel symmetric second-order covariant tensors

Explicit example in arbitrary dimension

Abstract

A generalization of Ricci-like solitons with torse-forming potential, which is a constant multiple of the Reeb vector field, is studied. The conditions under which these solitons are equivalent to almost Einstein-like metrics are given. Some results are obtained for a parallel symmetric second-order covariant tensor. Finally, an explicit example of an arbitrary dimension is given and some of the results are illustrated.