Pair of Associated η -Ricci–Bourguignon Almost Solitons with Generalized Conformal Killing Potential on Sasaki-like Almost Contact Complex Riemannian Manifolds

Mancho Manev ()
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Mancho Manev: Department of Algebra and Geometry, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen St., 4000 Plovdiv, Bulgaria

Mathematics, 2025, vol. 13, issue 13, 1-12

Abstract: The subject of this study is almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds. The considerations are restricted to a special class of these manifolds, namely those of the Sasaki-like type, because of their geometric construction and the explicit expression of their classification tensor by the pair of B-metrics. Here, each of the two B-metrics is considered as an η -Ricci–Bourguignon almost soliton, where η is the contact form. The soliton potential is chosen to be a conformal Killing vector field (in particular, concircular or concurrent) and then a generalization of the notion of conformality using contact conformal transformations of B-metrics. The resulting manifolds, equipped with the introduced almost solitons, are geometrically characterized. In the five-dimensional case, an explicit example on a Lie group depending on two real parameters is constructed, and the properties obtained in the theoretical part are confirmed.

Keywords: η -Ricci–Bourguignon almost soliton; almost contact B-metric manifold; almost contact complex Riemannian manifold; Sasaki-like manifold; conformal Killing vector field (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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