Curvature form projective spaces

Question

Let $T\mathbb{C}P^n$ tangent bundle over $\mathbb{C}P^n$. We have an hermitian metric on $T \mathbb{C}P^n$ defined as $h=\frac{dzd\bar{z}}{(1+|z|^2)^2}$. If we consider Levi-Civita connection we can define the curvature form $\Omega:= d\omega + \frac{1}{2}[\omega,\omega]$, where $\omega$ is the connection form and $d$ the exterior derivative. How can I write the matrix of $\Omega$ in this situation? (For example for $n=2$).