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arXiv · 2411.00861

A rigidity result for axisymmetric toric Ricci solitons

Shiqiao Zhang
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Abstract

We examine a non-axisymmetric perturbation of a family of axisymmetric toric Einstein manifolds and Ricci solitons studied in Firester-Tsiamis (2024). We establish a rigidity result stating that these axisymmetric Ricci solitons do not admit constant-angle non-axisymmetric perturbations except for conformally flat cases. For these new cases, our result leads to an explicit description of the Einstein metrics and a classification of the Ricci solitons under a volume-collapsing ansatz.

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Shiqiao Zhang. 2024-10-30. A rigidity result for axisymmetric toric Ricci solitons. https://arxiv.org/abs/2411.00861

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