Expanding Ricci solitons coming out of weakly PIC1 metric cones
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929332670169088 |
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| author | Chan, Pak-Yeung Lee, Man-Chun Peachey, Luke T. |
| author_facet | Chan, Pak-Yeung Lee, Man-Chun Peachey, Luke T. |
| contents | Motivated by recent work of Deruelle-Schulze-Simon, we study complete weakly PIC1 Ricci flows with Euclidean volume growth coming out of metric cones. We show that such a Ricci flow must be an expanding gradient Ricci soliton, and as a consequence, any metric cone at infinity of a complete weakly PIC1 Kähler manifold with Euclidean volume growth is biholomorphic to complex Euclidean space in a canonical way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12755 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Expanding Ricci solitons coming out of weakly PIC1 metric cones Chan, Pak-Yeung Lee, Man-Chun Peachey, Luke T. Differential Geometry Motivated by recent work of Deruelle-Schulze-Simon, we study complete weakly PIC1 Ricci flows with Euclidean volume growth coming out of metric cones. We show that such a Ricci flow must be an expanding gradient Ricci soliton, and as a consequence, any metric cone at infinity of a complete weakly PIC1 Kähler manifold with Euclidean volume growth is biholomorphic to complex Euclidean space in a canonical way. |
| title | Expanding Ricci solitons coming out of weakly PIC1 metric cones |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2404.12755 |