Paper · Sep 1, 2025
Gradient Shrinking Sasaki-Ricci Solitons with Harmonic Weyl Tensor
As on arXiv
Abstract
We establish integral curvature estimates for complete gradient shrinking Sasaki-Ricci solitons. As an application, we show that any such soliton with harmonic Weyl tensor must be a finite quotient of a sphere. This result can be regarded as the Sasaki analogue of the work of Munteanu and Sesum [15] on Ricci solitons.
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Transverse Rigidity of Shrinking Sasaki-Ricci Solitons
Topics Sasakian & contact geometry, Ricci solitons · Same authors Shu-Cheng Chang, Hongbing Qiu · Shared terms “Sasaki Ricci”, “shrinking Sasaki”, “harmonic Weyl”
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Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons
Topics Sasakian & contact geometry, Ricci solitons · Same author Shu-Cheng Chang · Shared terms “shrinking Sasaki”, “Sasaki Ricci”, “gradient shrinking”
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Topics Sasakian & contact geometry, Ricci solitons · Same author Shu-Cheng Chang · Shared terms “Sasaki Ricci”
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Topics Sasakian & contact geometry, Ricci solitons · Same author Shu-Cheng Chang · Shared terms “Sasaki Ricci”
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The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor
Topics Ricci solitons · Shared terms “harmonic Weyl”, “Weyl tensor”
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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.