An example of compact K\"ahler manifold with nonnegative quadratic   bisectional curvature
  We construct a compact K\"ahler manifold of nonnegative quadratic bisectional curvature, which does not admit any K\"ahler metric of nonnegative orthogonal bisectional curvature. The manifold is a 7-dimensional K\"ahler C-space with second Betti number equal to 1, and its canonical metric is a K\"ahler-Einstein metric of positive scalar curvature 
Qun Li, Damin Wu, and Fangyang Zheng
math.DG