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<p>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.</p>

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On ricci solitons with isoparametric potential functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月20日

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  • Hung Tran,
  • Kazuo Yamazaki

摘要

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.