ON REAL BISECTIONAL CURVATURE AND KAHLER-RICCI FLOW

摘要

In their recent work, X. Yang and F. Zheng proved the positivity of a canonical line bundle for compact Hermitian manifolds with negative real bisectional curvature, a curvature condition they introduced that generalizes the holomorphic sectional curvature for Kahler manifolds. In this short note, we prove a new parabolic Schwarz lemma for Kahler-Ricci flow, and, as an application, we give an alternative proof to their theorems by using the Kahler-Ricci flow.