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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1687-9139 |