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.

Solved by gpt-5.6-sol high.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-118/1/e/solution