On projectivized vector bundles and positive holomorphic sectional curvature
We generalize a construction of Hitchin to prove that, given any compact Kähler manifold M with positive holomorphic sectional curvature and any holomorphic vector bundle E over M, the projectivized vector bundle {\mathbb{P}}(E) admits a Kähler metric with positive holomorphic sectional curvature.
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| Veröffentlicht in: | Proceedings of the American Mathematical Society 2018-07, Vol.146 (7), p.2877-2882 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We generalize a construction of Hitchin to prove that, given any compact Kähler manifold M with positive holomorphic sectional curvature and any holomorphic vector bundle E over M, the projectivized vector bundle {\mathbb{P}}(E) admits a Kähler metric with positive holomorphic sectional curvature. |
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| ISSN: | 0002-9939 1088-6826 |
| DOI: | 10.1090/proc/13868 |