Riemann soliton within the framework of contact geometry
M.N. Devaraja, H. Aruna Kumara, V. Venkatesha
Abstract
In this paper, we study contact metric manifold whose metric is a Riemann soliton. First, we consider Riemann soliton (g, V ) with V as contact vector field on a Sasakian manifold (M, g) and in this case we prove that M is either of constant curvature +1 (and V is Killing) or D-homothetically fixed η-Einstein manifold (and V leaves the structure tensor φ invariant). Next, we prove that if a compact K-contact manifold whose metric g is a gradient almost Riemann soliton, then it is Sasakian and isometric to a unit sphere S2n+1. Further, we study H-contact manifold admitting a Riemann soliton (g, V ) where V is pointwise collinear with ξ.
Topics & Concepts
MathematicsSolitonManifold (fluid mechanics)Riemann curvature tensorRiemann hypothesisRiemann surfacePointwiseMathematical analysisVector fieldRiemann sphereMathematical physicsPure mathematicsCurvatureGeometryPhysicsQuantum mechanicsNonlinear systemMechanical engineeringEngineeringGeometric Analysis and Curvature FlowsGeometry and complex manifoldsGeometric and Algebraic Topology