On the fundamental group of steady gradient Ricci solitons with nonnegative sectional curvature
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909597915152384 |
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| author | Deng, Yuxing Hao, Yuehan |
| author_facet | Deng, Yuxing Hao, Yuehan |
| contents | In this paper, we study the fundamental group of the complete steady gradient Ricci soliton with nonnegative sectional curvature. We prove that the fundamental group of such a Ricci soliton is either trivial or infinite. As a corollary, we show that an $n$-dimensional complete $κ$-noncollapsed steady gradient Ricci soliton with nonnegative sectional curvature must be diffeomorphic to $\mathbb{R}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07452 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the fundamental group of steady gradient Ricci solitons with nonnegative sectional curvature Deng, Yuxing Hao, Yuehan Differential Geometry In this paper, we study the fundamental group of the complete steady gradient Ricci soliton with nonnegative sectional curvature. We prove that the fundamental group of such a Ricci soliton is either trivial or infinite. As a corollary, we show that an $n$-dimensional complete $κ$-noncollapsed steady gradient Ricci soliton with nonnegative sectional curvature must be diffeomorphic to $\mathbb{R}^n$. |
| title | On the fundamental group of steady gradient Ricci solitons with nonnegative sectional curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2412.07452 |