Ricci almost solitons with associated projective vector field
Ramesh Sharma, Sharief Deshmukh
Abstract
Abstract A Ricci almost soliton whose associated vector field is projective is shown to have vanishing Cotton tensor, divergence-free Bach tensor and Ricci tensor as conformal Killing. For the compact case, a sharp inequality is obtained in terms of scalar curvature.We show that every complete gradient Ricci soliton is isometric to the Riemannian product of a Euclidean space and an Einstein space. A complete K -contact Ricci almost soliton whose associated vector field is projective is compact Einstein and Sasakian.
Topics & Concepts
MathematicsRicci curvatureScalar curvatureRiemann curvature tensorRicci decompositionRicci flowVector fieldWeyl tensorEinstein tensorPure mathematicsMathematical analysisMathematical physicsEinstein manifoldCurvatureGeometryGeometric Analysis and Curvature FlowsGeometry and complex manifoldsAdvanced Differential Geometry Research