The form $iF_\nabla$ is the <Ricci form of a Kähler manifold>. In complex dimension one, $iF_\nabla=K_g\omega_X=\frac12\operatorname{Scal}_g\omega_X$. Thus
$$
\lambda=K_g=\frac12\operatorname{Scal}_g,
$$
where $K_g$ is the Gaussian curvature.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 118 / 1 / e / Solution

{c}
{title2=$\rho$}
{wiki=Ricci_curvature#Kähler_manifolds}

The Ricci form is the real curvature form $iF_\nabla$ of the Chern connection on $T^{1,0}X$. In complex dimension one, $\rho=K\omega=\frac12\operatorname{Scal}\,\omega$.


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