K\"ahler C-spaces and quadratic bisectional curvature

In this article we give necessary and sufficient conditions for an irreducible K"ahler C-space with $b_2=1$ to have nonnegative or positive quadratic bisectional curvature, assuming the space is not Hermitian symmetric. In the cases of the five exceptional Lie groups $E_6,E_7,E_8,F_4,G_2$, the computer package MAPLE is used to assist our calculations. The results are related to two conjectures of Li-Wu-Zheng.