Kahler manifolds with positive orthogonal Ricci curvature

The orthogonal Ricci curvature of a tangent direction in a Kahler manifold is the difference between the Ricci and the holomorphic sectional curvature of that direction. This curvature notion is closely related to Ricci and holomorphic sectional curvature. We are interested in understanding the class of compact Kahler manifolds with everywhere positive orthogonal Ricci curvature. In this talk, I will report on some recent progress on the topic.