\( \ast \)-conformal \(\eta \)-Ricci soliton on Sasakian manifold. (English) Zbl 1528.53034
Summary: In this paper, we study \(\ast \)-Conformal \(\eta \)-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting \(\ast \)-Conformal \(\eta \)-Ricci soliton. We obtain some significant results on \(\ast \)-Conformal \(\eta \)-Ricci soliton in Sasakian manifolds satisfying \(R(\xi,X)\cdot S=0\), \(S(\xi,X)\cdot R=0\), \(\overline{P}(\xi,X)\cdot S=0\), where \(\overline{P}\) is Pseudo-projective curvature tensor. The conditions for \(\ast \)-Conformal \(\eta \)-Ricci soliton on \(\phi \)-conharmonically flat and \(\phi \)-projectively flat Sasakian manifolds have been obtained in this paper. Lastly we give an example of five-dimensional Sasakian manifolds satisfying \(\ast \)-Conformal \(\eta \)-Ricci soliton.
MSC:
| 53C18 | Conformal structures on manifolds |
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53D15 | Almost contact and almost symplectic manifolds |
Keywords:
\( \ast \)-conformal \(\eta \)-Ricci solitons; \( \eta \)-Einstein manifolds; Sasakian manifoldsReferences:
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