Yamabe Solitons on Conformal Almost-Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field
A Yamabe soliton is considered on an almost-contact complex Riemannian manifold (also known as an almost-contact B-metric manifold), which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. A case in which t...
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MDPI AG
2023-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/1/44 |
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| author | Mancho Manev |
| author_facet | Mancho Manev |
| author_sort | Mancho Manev |
| collection | DOAJ |
| description | A Yamabe soliton is considered on an almost-contact complex Riemannian manifold (also known as an almost-contact B-metric manifold), which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. A case in which the potential is a torse-forming vector field of constant length on the vertical distribution determined by the Reeb vector field is studied. In this way, manifolds from one of the main classes of the studied manifolds are obtained. The same class contains the conformally equivalent manifolds of cosymplectic manifolds by the usual conformal transformation of the given B-metric. An explicit five-dimensional example of a Lie group is given, which is characterized in relation to the obtained results. |
| first_indexed | 2024-03-09T13:36:39Z |
| format | Article |
| id | doaj.art-09994d1d60e147d6849ac8211528ab52 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:36:39Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-09994d1d60e147d6849ac8211528ab522023-11-30T21:11:32ZengMDPI AGAxioms2075-16802023-01-011214410.3390/axioms12010044Yamabe Solitons on Conformal Almost-Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector FieldMancho Manev0Department of Algebra and Geometry, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen St, 4000 Plovdiv, BulgariaA Yamabe soliton is considered on an almost-contact complex Riemannian manifold (also known as an almost-contact B-metric manifold), which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. A case in which the potential is a torse-forming vector field of constant length on the vertical distribution determined by the Reeb vector field is studied. In this way, manifolds from one of the main classes of the studied manifolds are obtained. The same class contains the conformally equivalent manifolds of cosymplectic manifolds by the usual conformal transformation of the given B-metric. An explicit five-dimensional example of a Lie group is given, which is characterized in relation to the obtained results.https://www.mdpi.com/2075-1680/12/1/44Yamabe solitonalmost-contact B-metric manifoldalmost-contact complex Riemannian manifoldtorse-forming vector fieldcontact conformal transformations |
| spellingShingle | Mancho Manev Yamabe Solitons on Conformal Almost-Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field Axioms Yamabe soliton almost-contact B-metric manifold almost-contact complex Riemannian manifold torse-forming vector field contact conformal transformations |
| title | Yamabe Solitons on Conformal Almost-Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field |
| title_full | Yamabe Solitons on Conformal Almost-Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field |
| title_fullStr | Yamabe Solitons on Conformal Almost-Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field |
| title_full_unstemmed | Yamabe Solitons on Conformal Almost-Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field |
| title_short | Yamabe Solitons on Conformal Almost-Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field |
| title_sort | yamabe solitons on conformal almost contact complex riemannian manifolds with vertical torse forming vector field |
| topic | Yamabe soliton almost-contact B-metric manifold almost-contact complex Riemannian manifold torse-forming vector field contact conformal transformations |
| url | https://www.mdpi.com/2075-1680/12/1/44 |
| work_keys_str_mv | AT manchomanev yamabesolitonsonconformalalmostcontactcomplexriemannianmanifoldswithverticaltorseformingvectorfield |