Geometry and Topology of Gradient 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_ | 1866908965392089088 |
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| author | Chang, Shu-Cheng Han, Yingbo Wu, Chin-Tung |
| author_facet | Chang, Shu-Cheng Han, Yingbo Wu, Chin-Tung |
| contents | In this paper, we study the geometry and topology of complete gradient shrinking Sasaki-Ricci solitons. We first prove that they must be connected at infinity. This is a Sasaki analogue of gradient shrinking Kähler-Ricci solitons. Secondly, with the positive sectional curvature or positive transverse holomorphic bisectional curvature, we show that they must be compact. All results are served as a generalization of Perelman in dimension three, of Naber in dimension four, and of Munteanu-Wang in all dimensions, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons Chang, Shu-Cheng Han, Yingbo Wu, Chin-Tung Differential Geometry In this paper, we study the geometry and topology of complete gradient shrinking Sasaki-Ricci solitons. We first prove that they must be connected at infinity. This is a Sasaki analogue of gradient shrinking Kähler-Ricci solitons. Secondly, with the positive sectional curvature or positive transverse holomorphic bisectional curvature, we show that they must be compact. All results are served as a generalization of Perelman in dimension three, of Naber in dimension four, and of Munteanu-Wang in all dimensions, respectively. |
| title | Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2508.13495 |