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

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Listed:
  • Abdul Haseeb
  • Meraj Ali Khan

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.

Suggested Citation

  • Abdul Haseeb & Meraj Ali Khan, 2022. "Conformal η‐Ricci‐Yamabe Solitons within the Framework of ϵ‐LP‐Sasakian 3‐Manifolds," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:3847889
    DOI: 10.1155/2022/3847889
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    References listed on IDEAS

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    1. Xu Xufeng & Chao Xiaoli, 1998. "Two theorems on ( ϵ ) -Sasakian manifolds," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 21, pages 1-6, January.
    2. D. H. Jin, 2010. "Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(4), pages 569-581, August.
    3. A. Bejancu & K. L. Duggal, 1993. "Real hypersurfaces of indefinite Kaehler manifolds," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 16, pages 1-12, January.
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