Almost Ricci–Yamabe soliton on contact metric manifolds
Purpose – This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds. Design/methodology/approach – The paper is designed as follows: In Section 3, a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator adm...
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Emerald Publishing
2025-01-01
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| Series: | Arab Journal of Mathematical Sciences |
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| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-07-2022-0171/full/pdf |
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| author | Mohan Khatri Jay Prakash Singh |
| author_facet | Mohan Khatri Jay Prakash Singh |
| author_sort | Mohan Khatri |
| collection | DOAJ |
| description | Purpose – This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds. Design/methodology/approach – The paper is designed as follows: In Section 3, a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator admitting almost Ricci–Yamabe soliton is considered. In Section 4, a complete K-contact manifold admits gradient Ricci–Yamabe soliton is studied. Then in Section 5, gradient almost Ricci–Yamabe soliton in non-Sasakian (k, μ)-contact metric manifold is assumed. Moreover, the obtained result is verified by constructing an example. Findings – We prove that if the metric g admits an almost (α, β)-Ricci–Yamabe soliton with α ≠ 0 and potential vector field collinear with the Reeb vector field ξ on a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator, then the manifold is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field ξ. For the case of complete K-contact, we found that it is isometric to unit sphere S2n+1 and in the case of (k, μ)-contact metric manifold, it is flat in three-dimension and locally isometric to En+1 × Sn(4) in higher dimension. Originality/value – All results are novel and generalizations of previously obtained results. |
| format | Article |
| id | doaj-art-67dda94f503c4f1093b9f08bff8e7def |
| institution | Kabale University |
| issn | 1319-5166 2588-9214 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj-art-67dda94f503c4f1093b9f08bff8e7def2025-01-24T04:22:17ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142025-01-0131111812910.1108/AJMS-07-2022-0171Almost Ricci–Yamabe soliton on contact metric manifoldsMohan Khatri0Jay Prakash Singh1Department of Mathematics and Computer Science, Mizoram University, Aizawl, IndiaMizoram University, Aizawl, IndiaPurpose – This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds. Design/methodology/approach – The paper is designed as follows: In Section 3, a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator admitting almost Ricci–Yamabe soliton is considered. In Section 4, a complete K-contact manifold admits gradient Ricci–Yamabe soliton is studied. Then in Section 5, gradient almost Ricci–Yamabe soliton in non-Sasakian (k, μ)-contact metric manifold is assumed. Moreover, the obtained result is verified by constructing an example. Findings – We prove that if the metric g admits an almost (α, β)-Ricci–Yamabe soliton with α ≠ 0 and potential vector field collinear with the Reeb vector field ξ on a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator, then the manifold is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field ξ. For the case of complete K-contact, we found that it is isometric to unit sphere S2n+1 and in the case of (k, μ)-contact metric manifold, it is flat in three-dimension and locally isometric to En+1 × Sn(4) in higher dimension. Originality/value – All results are novel and generalizations of previously obtained results.https://www.emerald.com/insight/content/doi/10.1108/AJMS-07-2022-0171/full/pdfRicci solitonYamabe soliton(k, μ)-Contact metric manifoldRicci–Yamabe solitonContact geometry |
| spellingShingle | Mohan Khatri Jay Prakash Singh Almost Ricci–Yamabe soliton on contact metric manifolds Arab Journal of Mathematical Sciences Ricci soliton Yamabe soliton (k, μ)-Contact metric manifold Ricci–Yamabe soliton Contact geometry |
| title | Almost Ricci–Yamabe soliton on contact metric manifolds |
| title_full | Almost Ricci–Yamabe soliton on contact metric manifolds |
| title_fullStr | Almost Ricci–Yamabe soliton on contact metric manifolds |
| title_full_unstemmed | Almost Ricci–Yamabe soliton on contact metric manifolds |
| title_short | Almost Ricci–Yamabe soliton on contact metric manifolds |
| title_sort | almost ricci yamabe soliton on contact metric manifolds |
| topic | Ricci soliton Yamabe soliton (k, μ)-Contact metric manifold Ricci–Yamabe soliton Contact geometry |
| url | https://www.emerald.com/insight/content/doi/10.1108/AJMS-07-2022-0171/full/pdf |
| work_keys_str_mv | AT mohankhatri almostricciyamabesolitononcontactmetricmanifolds AT jayprakashsingh almostricciyamabesolitononcontactmetricmanifolds |