Conformal η-Ricci-Yamabe Solitons within the Framework of ϵ-LP-Sasakian 3-Manifolds
In the present note, we study ϵ-LP-Sasakian 3-manifolds M3ϵ whose metrics are conformal η-Ricci-Yamabe solitons (in short, CERYS), and it is proven that if an M3ϵ with a constant scalar curvature admits a CERYS, then £Uζ is orthogonal to ζ if and only if Λ−ϵσ=−2ϵl+mr/2+1/2p+2/3. Further, we study gr...
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Wiley
2022-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/3847889 |
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| author | Abdul Haseeb Meraj Ali Khan |
| author_facet | Abdul Haseeb Meraj Ali Khan |
| author_sort | Abdul Haseeb |
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| description | In the present note, we study ϵ-LP-Sasakian 3-manifolds M3ϵ whose metrics are conformal η-Ricci-Yamabe solitons (in short, CERYS), and it is proven that if an M3ϵ with a constant scalar curvature admits a CERYS, then £Uζ is orthogonal to ζ if and only if Λ−ϵσ=−2ϵl+mr/2+1/2p+2/3. Further, we study gradient CERYS in M3ϵ and proved that an M3ϵ admitting gradient CERYS is a generalized conformal η-Einstein manifold; moreover, the gradient of the potential function is pointwise collinear with the Reeb vector field ζ. Finally, the existence of CERYS in an M3ϵ has been drawn by a concrete example. |
| format | Article |
| id | doaj-art-e11e2452ec6f4c929ef55c0c9e9085a6 |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-e11e2452ec6f4c929ef55c0c9e9085a62025-02-03T06:11:50ZengWileyAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/3847889Conformal η-Ricci-Yamabe Solitons within the Framework of ϵ-LP-Sasakian 3-ManifoldsAbdul Haseeb0Meraj Ali Khan1Department of MathematicsDepartment of MathematicsIn the present note, we study ϵ-LP-Sasakian 3-manifolds M3ϵ whose metrics are conformal η-Ricci-Yamabe solitons (in short, CERYS), and it is proven that if an M3ϵ with a constant scalar curvature admits a CERYS, then £Uζ is orthogonal to ζ if and only if Λ−ϵσ=−2ϵl+mr/2+1/2p+2/3. Further, we study gradient CERYS in M3ϵ and proved that an M3ϵ admitting gradient CERYS is a generalized conformal η-Einstein manifold; moreover, the gradient of the potential function is pointwise collinear with the Reeb vector field ζ. Finally, the existence of CERYS in an M3ϵ has been drawn by a concrete example.http://dx.doi.org/10.1155/2022/3847889 |
| spellingShingle | Abdul Haseeb Meraj Ali Khan Conformal η-Ricci-Yamabe Solitons within the Framework of ϵ-LP-Sasakian 3-Manifolds Advances in Mathematical Physics |
| title | Conformal η-Ricci-Yamabe Solitons within the Framework of ϵ-LP-Sasakian 3-Manifolds |
| title_full | Conformal η-Ricci-Yamabe Solitons within the Framework of ϵ-LP-Sasakian 3-Manifolds |
| title_fullStr | Conformal η-Ricci-Yamabe Solitons within the Framework of ϵ-LP-Sasakian 3-Manifolds |
| title_full_unstemmed | Conformal η-Ricci-Yamabe Solitons within the Framework of ϵ-LP-Sasakian 3-Manifolds |
| title_short | Conformal η-Ricci-Yamabe Solitons within the Framework of ϵ-LP-Sasakian 3-Manifolds |
| title_sort | conformal η ricci yamabe solitons within the framework of ϵ lp sasakian 3 manifolds |
| url | http://dx.doi.org/10.1155/2022/3847889 |
| work_keys_str_mv | AT abdulhaseeb conformalēricciyamabesolitonswithintheframeworkofelpsasakian3manifolds AT merajalikhan conformalēricciyamabesolitonswithintheframeworkofelpsasakian3manifolds |