Construction of higher-dimensional ALF Calabi-Yau metrics
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909354917101568 |
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| author | Min, Daheng |
| author_facet | Min, Daheng |
| contents | Roughly speaking, an ALF metric of real dimension 4n should be a metric such that it has a (4n-1)-dimensional asymptotic cone, the volume growth of this metric is of order 4n-1 and its sectional curvature tends to 0 at infinity. In this paper, we first show that the Taub-NUT deformation of a hyperkähler cone with respect to a locally free S1-symmetry is ALF hyperkähler. Using this metric at infinity, we establish the existence of ALF Calabi-Yau metric on certain crepant resolutions. In particular, we prove that there exist ALF Calabi-Yau metrics on canonical bundles of classical homogeneous Fano contact manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_01866 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Construction of higher-dimensional ALF Calabi-Yau metrics Min, Daheng Differential Geometry 53C25 (Primary) 53C55, 53C26, 53C30, 53D20 (Secondary) Roughly speaking, an ALF metric of real dimension 4n should be a metric such that it has a (4n-1)-dimensional asymptotic cone, the volume growth of this metric is of order 4n-1 and its sectional curvature tends to 0 at infinity. In this paper, we first show that the Taub-NUT deformation of a hyperkähler cone with respect to a locally free S1-symmetry is ALF hyperkähler. Using this metric at infinity, we establish the existence of ALF Calabi-Yau metric on certain crepant resolutions. In particular, we prove that there exist ALF Calabi-Yau metrics on canonical bundles of classical homogeneous Fano contact manifolds. |
| title | Construction of higher-dimensional ALF Calabi-Yau metrics |
| topic | Differential Geometry 53C25 (Primary) 53C55, 53C26, 53C30, 53D20 (Secondary) |
| url | https://arxiv.org/abs/2306.01866 |