As on arXiv
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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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Gradient Shrinking Sasaki-Ricci Solitons with Harmonic Weyl Tensor
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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Gradient Shrinking Sasaki-Ricci Solitons on Sasakian Manifolds of Dimension Up to Seven
Topics Sasakian & contact geometry, Singularities, Ricci solitons · Same authors Shu-Cheng Chang, Chien Lin · Shared terms “Sasaki Ricci”, “shrinking Sasaki”, “transverse”
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Convergence of the Sasaki-Ricci flow on Sasakian 5-manifolds of general type
Topics Sasakian & contact geometry, Singularities · Same authors Shu-Cheng Chang, Chien Lin · Shared terms “Sasaki Ricci”, “transverse”, “Einstein”
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On the Hamilton-Tian Conjecture in a compact transverse Fano Sasakian -manifold
Topics Sasakian & contact geometry, Singularities, Ricci solitons · Same authors Shu-Cheng Chang, Chien Lin · Shared terms “Sasaki Ricci”, “transverse”, “Sasaki Einstein”
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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 “Sasaki Ricci”, “shrinking Sasaki”, “transverse”
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Foliation divisorial contraction by the Sasaki-Ricci flow on Sasakian 5-manifolds
Topics Sasakian & contact geometry, Singularities · Same authors Shu-Cheng Chang, Chien Lin · Shared terms “Sasaki Ricci”, “quotient”
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On the existence of conic Sasaki-Einstein metrics on log Fano Sasakian manifolds of dimension five
Topics Sasakian & contact geometry, Ricci solitons · Same authors Shu-Cheng Chang, Fengjiang Li, Chien Lin · Shared terms “Sasaki Ricci”, “Sasaki Einstein”, “transverse”
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Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature
Topics Scalar curvature, Stability & uniqueness, Ricci solitons · Same author Fengjiang Li · Shared terms “constant scalar”, “finite quotient”
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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.4Blow-Ups, Blow-Downs and Splitting at Infinity
Limits of rescaled manifolds and flows: why blow-up limits are nonnegatively curved, what blow-downs see, and how lines appear at infinity.
- 11B.6Rotationally Symmetric Flows and the Standard Solution
The neckpinch in equations: warped products under the flow, what the maximum principle forces, and the standard solution that surgery glues in.
- 6C.4The Yamabe Problem and Critical Exponents
Conformal changes of scalar curvature, the Yamabe functional, Aubin's threshold and Schoen's solution, concentration compactness and bubbles, and why Perelman's log-Sobolev minimisers always exist.