Transverse Rigidity of Shrinking Sasaki-Ricci Solitons
Differential Geometry
2026-05-04 v2
Abstract
In this paper, we study several properties of Sasaki-Ricci solitons as singularity models of the Sasaki-Ricci flow. First, we establish several fundamental equations for Sasaki-Ricci solitons, which enable us to derive potential estimates and prove the positivity of the scalar curvature. Then we present two criteria for the transverse rigidity of Sasaki-Ricci solitons. As essential applications, we prove that any low-dimensional Sasaki-Ricci soliton with constant scalar curvature must be Sasaki-Einstein, and that any Sasaki-Ricci soliton with harmonic Weyl tensor is a finite quotient of the sphere.
Cite
@article{arxiv.2502.16148,
title = {Transverse Rigidity of Shrinking Sasaki-Ricci Solitons},
author = {Shu-Cheng Chang and Fengjiang Li and Chien Lin and Hongbing Qiu},
journal= {arXiv preprint arXiv:2502.16148},
year = {2026}
}