Suppose $\omega$ is a Kähler metric of constant scalar curvature with positive bisectional curvature, how to prove $\omega$ is Kähler-Einstein?
I was told that we can use the following method:
Step 1: Use Bochner tecnique to prove $\dim H^2=1$
Step 2: Constant scalar curvature $\implies$ Ricci curvature is coclosed.
Step 3: Using Hodge theorem to derive the result.
How can we prove this in detail? Or where can I find further reference for this?
I heard this is a famous result from Hongxi Wu and his partner, and it can be proved using Weitzenbock method.