On some applications of Gauduchon metrics

Abstract

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.

13 pages, comments welcome

References in corpus (4)

• Gauduchon metrics with prescribed volume form
• The Monge-Ampère equation for non-integrable almost complex structures
• On Chern-Yamabe problem
• Remarks on Chern-Einstein Hermitian metrics

Cited by in corpus (1)

• Singular Gauduchon metrics