Transverse Rigidity of Shrinking Sasaki-Ricci Solitons
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915971237675008 |
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| author | Chang, Shu-Cheng Li, Fengjiang Lin, Chien Qiu, Hongbing |
| author_facet | Chang, Shu-Cheng Li, Fengjiang Lin, Chien Qiu, Hongbing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16148 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transverse Rigidity of Shrinking Sasaki-Ricci Solitons Chang, Shu-Cheng Li, Fengjiang Lin, Chien Qiu, Hongbing Differential Geometry 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. |
| title | Transverse Rigidity of Shrinking Sasaki-Ricci Solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2502.16148 |