On the Weighted Orthogonal Ricci curvature

We introduce the weighted orthogonal Ricci curvature – a two-parameter version of Ni–Zheng's curvature. This serves as very natural object in study relationship between curvature(s) and holomorphic sectional In particular, determining optimal constraints for compact Kähler manifold to be projective. this direction, we prove number vanishing theorems using both Hermitian category.