Mean curvature positivity and rational connectedness
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866929620775862272 |
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| author | Li, Chao Zhang, Chuanjing Zhang, Xi |
| author_facet | Li, Chao Zhang, Chuanjing Zhang, Xi |
| contents | In this paper, we use Uhlenbeck-Yau's continuity method to establish the correspondence between the mean curvature positivity and the HN-positivity on holomorphic vector bundles over compact Hermitian manifolds. As its application, we get a differential geometric criterion for rational connectedness, i.e. we prove that a compact Kähler manifold is projective and rationally connected if and only if its holomorphic tangent bundle is mean curvature positive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_00488 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Mean curvature positivity and rational connectedness Li, Chao Zhang, Chuanjing Zhang, Xi Differential Geometry 53C07, 14J60, 32Q15 In this paper, we use Uhlenbeck-Yau's continuity method to establish the correspondence between the mean curvature positivity and the HN-positivity on holomorphic vector bundles over compact Hermitian manifolds. As its application, we get a differential geometric criterion for rational connectedness, i.e. we prove that a compact Kähler manifold is projective and rationally connected if and only if its holomorphic tangent bundle is mean curvature positive. |
| title | Mean curvature positivity and rational connectedness |
| topic | Differential Geometry 53C07, 14J60, 32Q15 |
| url | https://arxiv.org/abs/2112.00488 |