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A rigidity result for axisymmetric toric Ricci solitons

Differential Geometry 2024-11-05 v1

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.

Keywords

Cite

@article{arxiv.2411.00861,
  title  = {A rigidity result for axisymmetric toric Ricci solitons},
  author = {Shiqiao Zhang},
  journal= {arXiv preprint arXiv:2411.00861},
  year   = {2024}
}

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7 pages