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arXiv · 2502.16148

Transverse Rigidity of Shrinking Sasaki-Ricci Solitons

Shu-Cheng Chang·Fengjiang Li·Chien Lin·Hongbing Qiu
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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.

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Shu-Cheng Chang, Fengjiang Li, Chien Lin, Hongbing Qiu. 2025-02-22. Transverse Rigidity of Shrinking Sasaki-Ricci Solitons. https://arxiv.org/abs/2502.16148

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