Connections, metrics and Higgs fields on complex fiber bundles
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908834678702080 |
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| author | Li, Nianzi Sheng, Mao |
| author_facet | Li, Nianzi Sheng, Mao |
| contents | We give a representation of the extension class associated to a holomorphic fibration by curvature, generalizing the work of Atiyah on holomorphic principal bundles in a natural way. As an application, we obtain a nonlinear analogue of the classical result of Weil on characterizing the existence of flat connections on holomorphic vector bundles over compact Riemann surfaces. We further establish a faithful functor from the category of nonlinear flat bundles reductive of Kähler type to the category of nonlinear Higgs bundles over the same base, which is assumed to be a compact complex manifold of Kähler type. Finally, we establish a notion of nonlinear harmonic bundle and prove that the variation of nonabelian Hodge structure is a nonlinear harmonic bundle in the rank one case and in the semisimple case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13838 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Connections, metrics and Higgs fields on complex fiber bundles Li, Nianzi Sheng, Mao Differential Geometry 53C05, 58D27 We give a representation of the extension class associated to a holomorphic fibration by curvature, generalizing the work of Atiyah on holomorphic principal bundles in a natural way. As an application, we obtain a nonlinear analogue of the classical result of Weil on characterizing the existence of flat connections on holomorphic vector bundles over compact Riemann surfaces. We further establish a faithful functor from the category of nonlinear flat bundles reductive of Kähler type to the category of nonlinear Higgs bundles over the same base, which is assumed to be a compact complex manifold of Kähler type. Finally, we establish a notion of nonlinear harmonic bundle and prove that the variation of nonabelian Hodge structure is a nonlinear harmonic bundle in the rank one case and in the semisimple case. |
| title | Connections, metrics and Higgs fields on complex fiber bundles |
| topic | Differential Geometry 53C05, 58D27 |
| url | https://arxiv.org/abs/2602.13838 |