On open manifolds admitting no complete metric with positive scalar curvature
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917853987340288 |
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| author | Shi, Yuguang Wang, Jian Wu, Runzhang Zhu, Jintian |
| author_facet | Shi, Yuguang Wang, Jian Wu, Runzhang Zhu, Jintian |
| contents | In this paper, we investigate the topological obstruction problem for positive scalar curvature and uniformly positive scalar curvature on open manifolds. We present a definition for open Schoen-Yau-Schick manifolds and prove that there is no complete metric with positive scalar curvature on these manifolds. Similarly, we define weak Schoen-Yau-Shick manifolds by analogy, which are expected to admit no complete metrics with uniformly positive scalar curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On open manifolds admitting no complete metric with positive scalar curvature Shi, Yuguang Wang, Jian Wu, Runzhang Zhu, Jintian Differential Geometry 00X99 In this paper, we investigate the topological obstruction problem for positive scalar curvature and uniformly positive scalar curvature on open manifolds. We present a definition for open Schoen-Yau-Schick manifolds and prove that there is no complete metric with positive scalar curvature on these manifolds. Similarly, we define weak Schoen-Yau-Shick manifolds by analogy, which are expected to admit no complete metrics with uniformly positive scalar curvature. |
| title | On open manifolds admitting no complete metric with positive scalar curvature |
| topic | Differential Geometry 00X99 |
| url | https://arxiv.org/abs/2404.01660 |