Conformal η‐Ricci‐Yamabe Solitons within the Framework of ϵ‐LP‐Sasakian 3‐Manifolds

Abdul Haseeb and Meraj Ali Khan

Advances in Mathematical Physics, 2022, vol. 2022, issue 1

Abstract: In the present note, we study ϵ‐LP‐Sasakian 3‐manifolds M3(ϵ) whose metrics are conformal η‐Ricci‐Yamabe solitons (in short, CERYS), and it is proven that if an M3(ϵ) with a constant scalar curvature admits a CERYS, then £Uζ is orthogonal to ζ if and only if Λ − ϵσ = −2ϵl + (mr/2) + (1/2)(p + (2/3)). Further, we study gradient CERYS in M3(ϵ) and proved that an M3(ϵ) 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 M3(ϵ) has been drawn by a concrete example.

Date: 2022
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https://doi.org/10.1155/2022/3847889

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:3847889

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