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arXiv · 2506.03545

On Ricci Solitons with Isoparametric Potential Functions

Hung Tran·Kazuo Yamazaki
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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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Hung Tran, Kazuo Yamazaki. 2025-06-04. On Ricci Solitons with Isoparametric Potential Functions. https://doi.org/10.1007/s00209-025-03933-1

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