  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 K\"ahler manifold.
Moreover, the scalar curvature controls full curvature for this type of
metrics.
