The Kähler-Ricci flow on Kähler manifolds with 2 traceless bisectional curvature operator

Abstract

It was proved by H. Chen earlier that the property of the sum of any two eigenvalues of the curvature operator is positive is preserved under the ricci flow in all dimensional. By a recent result of Phong-Sturm, a similar notion of positive 2-traceless bisectional curvature positive is preserved on complex surface. We prove that this holds in all dimensional Kähler manifold. Moreover, the scalar curvature controls full curvature for this type of metrics.

19 pages