I would like to know the intuition behind the holomorphic bisectional curvature of Hermitian manifolds. I already know that the classical sectional curvature of a Riemannian (not necessarily complex) manifold roughly tells us how geodesics spread apart. What is the analogue for holomorphic bisectional curvature? Do you know any reference, where I can read more about this?



Intuition for holomorphic bisectional curvature
Ngaiming Mok, [The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature,](http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jdg/1214441778) J. Differential Geom. Volume 27, Number 2 (1988), 179-214. 


Mok improves Mori's and Siu-Yau's proof of Fraenkel's conjecture claiming that a compact Kahler manifold with positive HBC is biholomorphic to ${\Bbb C} P^n$. He shows that any compact Kahler manifold with non-negative HBC is locally isometric to a product of symmetric spaces and ${\Bbb C} P^n$. It is interesting that Mok uses Hamilton's evolution equation (essentially the same as used by Perelman 15 years later).


