Cohomogeneity one Ricci Solitons from Hopf Fibrations

Abstract

This paper studies cohomogeneity one Ricci solitons. If the isotropy representation of the principal orbit $G/K$ consists of two inequivalent $A{d}_K$-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 Böhm. The techniques also apply to $m$-quasi-Einstein metrics.

34 pages, asymptotics refined

References in corpus (3)

• A family of non-collapsed steady Ricci solitons in even dimensions greater or equal to four
• Non-Kähler Expanding Ricci Solitons II
• Conformally Kähler geometry and quasi-Einstein metrics

Cited by in corpus (5)

• Field Correlator Method for the confinement in QCD
• Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature
• Invariant Ricci-flat Metrics of Cohomogeneity One with Wallach Spaces as Principal Orbits
• Cohomogeneity-One Quasi-Einstein Metrics
• Painlevé analysis of Ricci solitons over warped products