∗-<i>η</i>-Ricci Soliton within the Framework of Sasakian Manifold
Santu Dey, Soumendu Roy
Abstract
In this paper we study ∗-η-Ricci soliton on Sasakian manifolds. Here, we have discussed some curvature properties on Sasakian manifold admitting ∗-η-Ricci soliton. We have obtained some significant results on ∗-η-Ricci soliton in Sasakian manifolds satisfying R(ξ, X) · S = 0, S(ξ, X) · R = 0, P̄ (ξ, X) · S = 0, where P̄ is Pseudo-projective curvature tensor.The conditions for ∗-η-Ricci soliton on ϕ-conharmonically flat and ϕ-projectively flat Sasakian manifolds have been obtained in this article. Lastly, we have given an example of 5-dimensional Sasakian manifolds satisfying ∗-η-Ricci soliton.
Topics & Concepts
Ricci curvatureRicci decompositionSolitonMathematicsCurvature of Riemannian manifoldsEinstein manifoldManifold (fluid mechanics)Pure mathematicsRicci-flat manifoldRicci flowRiemann curvature tensorMathematical physicsMathematical analysisCurvaturePhysicsScalar curvatureSectional curvatureGeometryNonlinear systemQuantum mechanicsEngineeringMechanical engineeringGeometric Analysis and Curvature FlowsGeometry and complex manifoldsAdvanced Differential Geometry Research