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This is a Quantitative Study study.

October 7, 2025Open Access

Geometry of Shrinking Sasaki-Ricci Solitons I: Fundamental Equations and Characterization of Rigidity

Key Points

The study establishes fundamental equations for sasaki-ricci solutions, aiding in understanding their geometric properties.
It provides two criteria for transverse rigidity of sasaki-ricci solutions, offering insights into their structural behavior.
The findings indicate that low-dimensional sasaki-ricci solutions with constant scalar curvature must be sasaki-einstein.
This research highlights the potential relationship between sasaki-ricci flows and their singularity models.

Abstract

In this paper, we study some properties of Sasaki-Ricci soltions as the singularity models of Sasaki-Ricci flows. First, we establish some fundamental equations about the Sasaki-Ricci soltions which enable us to obtain the potential estimate and the positivity of the scalar curvature. Subsequently, two criteria about the transverse rigidity of Sasaki-Ricci soltions are given; and then, as an essential application, we prove that any Sasaki-Ricci soltion of low dimension with constant scalar curvature must be Sasaki-Einstein.

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