A note on the almost one half holomorphic pinching

Abstract

Motivated by a previous work of Zheng and the second named author, we study pinching constants of compact Kähler manifolds with positive holomorphic sectional curvature. In particular we prove a gap theorem following the work of Petersen and Tao on Riemannian manifolds with almost quarter-pinched sectional curvature.

6 pages. This is the version which the authors submitted to a journal for consideration for publication in June 2017. The reference has not been updated since then