Cohomogeneity one Ricci solitons from Hopf fibrations
Matthias Wink
Abstract
This paper studies cohomogeneity one Ricci solitons. If the isotropy representation of the principal orbit $G/K$ consists of two inequivalent $Ad_K$-invariant irreducible summands, the existence of parameter families of non-homothetic complete steady and expanding Ricci solitons on non-trivial bundles is shown. These examples were detected numerically by Buzano-Dancer-Gallaugher-Wang. The analysis of the corresponding Ricci flat trajectories is used to reconstruct Einstein metrics of positive scalar curvature due to B\"ohm. The techniques also apply to $m$-quasi-Einstein metrics.
Topics & Concepts
MathematicsHomothetic transformationScalar curvatureEinsteinIsotropyInvariant (physics)Pure mathematicsMathematical physicsRicci curvatureCurvatureMathematical analysisGeometryPhysicsQuantum mechanicsGeometric Analysis and Curvature FlowsGeometry and complex manifoldsAdvanced Differential Geometry Research