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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.16113 |
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| _version_ | 1866910291512524800 |
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| author | Arezzo, Claudio Li, Chao Loi, Andrea |
| author_facet | Arezzo, Claudio Li, Chao Loi, Andrea |
| contents | The aim of this paper is to study pointed Gromov-Hausdorff Convergence of sequences of Kähler submanifolds of a fixed Kähler ambient space. Our result shows that lower bounds on the scalar curvature imply convergence to a smooth Kähler manifold satisfying the same curvature bounds, and admitting a holomorphic isometry in the same ambient space. We then apply this convergence result to prove that there are no holomorphic isometries of a non-compact complete Kähler manifold with asymptotically non-negative ones into a finite dimensional complex projective space endowed with the Fubini-Study metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16113 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gromov-Hausdorff limits and Holomorphic isometries Arezzo, Claudio Li, Chao Loi, Andrea Differential Geometry 32Q40 The aim of this paper is to study pointed Gromov-Hausdorff Convergence of sequences of Kähler submanifolds of a fixed Kähler ambient space. Our result shows that lower bounds on the scalar curvature imply convergence to a smooth Kähler manifold satisfying the same curvature bounds, and admitting a holomorphic isometry in the same ambient space. We then apply this convergence result to prove that there are no holomorphic isometries of a non-compact complete Kähler manifold with asymptotically non-negative ones into a finite dimensional complex projective space endowed with the Fubini-Study metric. |
| title | Gromov-Hausdorff limits and Holomorphic isometries |
| topic | Differential Geometry 32Q40 |
| url | https://arxiv.org/abs/2306.16113 |