Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Curvature Properties of Almost Ricci-Like Solitons with Torse-Forming Vertical Potential on Almost Contact B-Metric Manifolds

Version 1 : Received: 4 February 2021 / Approved: 5 February 2021 / Online: 5 February 2021 (14:05:20 CET)

How to cite: MANEV, M. Curvature Properties of Almost Ricci-Like Solitons with Torse-Forming Vertical Potential on Almost Contact B-Metric Manifolds. Preprints 2021, 2021020164 (doi: 10.20944/preprints202102.0164.v1). MANEV, M. Curvature Properties of Almost Ricci-Like Solitons with Torse-Forming Vertical Potential on Almost Contact B-Metric Manifolds. Preprints 2021, 2021020164 (doi: 10.20944/preprints202102.0164.v1).

Abstract

A generalization of $\eta$-Ricci solitons is considered involving an additional metric and functions as soliton coefficients. The soliton potential is torse-forming and orthogonal to the contact distribution of the almost contact B-metric manifold. Then such a manifold can also be considered as an almost Einstein-like manifold, a generalization of an $\eta$-Einstein manifold with respect to both B-metrics and functions as coefficients. Necessary and sufficient conditions are found for a number of properties of the curvature tensor and its Ricci tensor of the studied manifolds. Finally, an explicit example of an arbitrary dimension is given and some of the results are illustrated.

Subject Areas

Almost Ricci-like soliton; almost $\eta$-Ricci soliton; almost Einstein-like manifold; almost $\eta$-Einstein manifold; almost contact B-metric manifold; torse-forming vector field

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