On Ricci Solitons with Isoparametric Potential Functions

Abstract

This paper studies a complete gradient Ricci soliton with an isoparametric potential function. Our first theorem asserts that, for the steady case, there is a critical level set of codimension greater than one. This is consistent with construction of cohomogeneity one models with singular orbits. There is a partial result for the shrinking case. We also study a particular ansatz of popular interest and obtain asymptotic behaviors.

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References in corpus (4)

• A compactness theorem for complete Ricci shrinkers
• Classification results for expanding and shrinking gradient Kähler-Ricci solitons
• Killing potentials with geodesic gradients on Kähler surfaces
• Ricci flow of warped Berger metrics on ${\mathbb{R}}^4$