On real bisectional curvature for Hermitian manifolds

Motivated by the recent work of Wu and Yau on the ampleness of a canonical line bundle for projective manifolds with negative holomorphic sectional curvature, we introduce a new curvature notion called real bisectional curvature for Hermitian manifolds. When the metric is Kähler, this is just the ho...

Full description

Saved in:
Bibliographic Details
Published in:Transactions of the American Mathematical Society 2019-04, Vol.371 (4), p.2703-2718
Main Authors: Yang, Xiaokui, Zheng, Fangyang
Format: Article
Language:English
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Motivated by the recent work of Wu and Yau on the ampleness of a canonical line bundle for projective manifolds with negative holomorphic sectional curvature, we introduce a new curvature notion called real bisectional curvature for Hermitian manifolds. When the metric is Kähler, this is just the holomorphic sectional curvature H, and when the metric is non-Kähler, it is slightly stronger than H. We classify compact Hermitian manifolds with constant nonzero real bisectional curvature, and also slightly extend Wu and Yau's theorem to the Hermitian case. The underlying reason for the extension is that the Schwarz lemma of Wu and Yau works the same when the target metric is only Hermitian but has nonpositive real bisectional curvature.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7445