Conformal η-Ricci almost solitons of Kenmotsu manifolds

Santu Dey, Siraj Uddin

2022International Journal of Geometric Methods in Modern Physics26 citationsDOI

Abstract

The aim of this paper is to find some important classes of Einstein manifolds using conformal [Formula: see text]-Ricci solitons and conformal [Formula: see text]-Ricci almost solitons. We prove that a Kenmotsu metric as conformal [Formula: see text]-Ricci soliton is Einstein if it is [Formula: see text]-Einstein or the potential vector field [Formula: see text] is infinitesimal contact transformation or collinear with the Reeb vector field [Formula: see text]. Next, we prove that a Kenmotsu metric as gradient conformal [Formula: see text]-Ricci almost soliton is Einstein if the Reeb vector field leaves the scalar curvature invariants. Finally, we construct some examples to illustrate the existence of conformal [Formula: see text]-Ricci soliton, gradient almost conformal [Formula: see text]-Ricci soliton on Kenmotsu manifold.

Topics & Concepts

Conformal mapScalar curvatureEinstein manifoldEinsteinMathematical physicsRicci curvatureMathematicsCurvature of Riemannian manifoldsVector fieldManifold (fluid mechanics)Ricci-flat manifoldCurvaturePure mathematicsPhysicsMathematical analysisSectional curvatureGeometryMechanical engineeringEngineeringGeometric Analysis and Curvature FlowsGeometry and complex manifoldsAdvanced Differential Geometry Research