Ricci–Bourguignon Almost Solitons with Vertical Torse-Forming Potential on Almost Contact Complex Riemannian Manifolds
Almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds, are equipped with Ricci–Bourguignon-like almost solitons. These almost solitons are a generalization of the known Ricci–Bourguignon almost solitons, in which, in addition to the main metric, the associated...
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2025-01-01
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| author | Mancho Manev |
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| description | Almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds, are equipped with Ricci–Bourguignon-like almost solitons. These almost solitons are a generalization of the known Ricci–Bourguignon almost solitons, in which, in addition to the main metric, the associated metric of the manifold is also involved. In the present paper, the soliton potential is specialized to be pointwise collinear with the Reeb vector field of the manifold structure, as well as torse-forming with respect to the two Levi-Civita connections of the pair of B-metrics. The forms of the Ricci tensor and the scalar curvatures generated by the pair of B-metrics on the studied manifolds with the additional structures have been found. In the three-dimensional case, an explicit example is constructed and some of the properties obtained in the theoretical part are illustrated. |
| format | Article |
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| institution | Kabale University |
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| language | English |
| publishDate | 2025-01-01 |
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| spelling | doaj-art-de51988993ba4be794a57d9977b8c96f2025-01-24T13:39:52ZengMDPI AGMathematics2227-73902025-01-0113224310.3390/math13020243Ricci–Bourguignon Almost Solitons with Vertical Torse-Forming Potential on Almost Contact Complex Riemannian ManifoldsMancho Manev0Department of Algebra and Geometry, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen St., 4000 Plovdiv, BulgariaAlmost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds, are equipped with Ricci–Bourguignon-like almost solitons. These almost solitons are a generalization of the known Ricci–Bourguignon almost solitons, in which, in addition to the main metric, the associated metric of the manifold is also involved. In the present paper, the soliton potential is specialized to be pointwise collinear with the Reeb vector field of the manifold structure, as well as torse-forming with respect to the two Levi-Civita connections of the pair of B-metrics. The forms of the Ricci tensor and the scalar curvatures generated by the pair of B-metrics on the studied manifolds with the additional structures have been found. In the three-dimensional case, an explicit example is constructed and some of the properties obtained in the theoretical part are illustrated.https://www.mdpi.com/2227-7390/13/2/243Ricci–Bourguignon almost solitonη-Ricci–Bourguignon almost solitonalmost contact B-metric manifoldalmost contact complex Riemannian manifoldtorse-forming vector fieldvertical potential |
| spellingShingle | Mancho Manev Ricci–Bourguignon Almost Solitons with Vertical Torse-Forming Potential on Almost Contact Complex Riemannian Manifolds Mathematics Ricci–Bourguignon almost soliton η-Ricci–Bourguignon almost soliton almost contact B-metric manifold almost contact complex Riemannian manifold torse-forming vector field vertical potential |
| title | Ricci–Bourguignon Almost Solitons with Vertical Torse-Forming Potential on Almost Contact Complex Riemannian Manifolds |
| title_full | Ricci–Bourguignon Almost Solitons with Vertical Torse-Forming Potential on Almost Contact Complex Riemannian Manifolds |
| title_fullStr | Ricci–Bourguignon Almost Solitons with Vertical Torse-Forming Potential on Almost Contact Complex Riemannian Manifolds |
| title_full_unstemmed | Ricci–Bourguignon Almost Solitons with Vertical Torse-Forming Potential on Almost Contact Complex Riemannian Manifolds |
| title_short | Ricci–Bourguignon Almost Solitons with Vertical Torse-Forming Potential on Almost Contact Complex Riemannian Manifolds |
| title_sort | ricci bourguignon almost solitons with vertical torse forming potential on almost contact complex riemannian manifolds |
| topic | Ricci–Bourguignon almost soliton η-Ricci–Bourguignon almost soliton almost contact B-metric manifold almost contact complex Riemannian manifold torse-forming vector field vertical potential |
| url | https://www.mdpi.com/2227-7390/13/2/243 |
| work_keys_str_mv | AT manchomanev riccibourguignonalmostsolitonswithverticaltorseformingpotentialonalmostcontactcomplexriemannianmanifolds |