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

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.

12 pages, v2: the first part of v1 under the condition for the constancy of k and clarification of the example

References in corpus (4)

• Almost $\eta$-Ricci and almost $\eta$-Yamabe solitons with torse-forming potential vector field
• On the structure tensors of almost contact B-metric manifolds
• Ricci-like solitons with vertical potential on Sasaki-like almost contact B-metric manifolds
• Lorentz Ricci solitons on 3-dimensional Lie groups

Cited by in corpus (1)

• Pairs of associated Yamabe almost solitons with vertical potential on almost contact complex Riemannian manifolds