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On some applications of Gauduchon metrics. (English) Zbl 1469.53110

Summary: We apply the existence and special properties of Gauduchon metrics to give several applications. The first one is concerned with the implications of algebro-geometric nature under the existence of a Hermitian metric with nonnegative holomorphic sectional curvature. The second one is to show the non-existence of holomorphic sections on Hermitian vector bundles under certain conditions. The third one is to give a restriction on the \(\partial \bar{\partial } \)-closedness of some real \((n - 1, n - 1)\)-forms on compact complex manifolds.

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
32Q10 Positive curvature complex manifolds
32L05 Holomorphic bundles and generalizations
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