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}
}
Comments
7 pages