Explicit construction of extremal Hermitian metrics with finite conical singularities on \(S^2\)
The authors construct a class of nonradial extremal Hermitian metrics with finite conical singular angles \(2\pi n_i\), \(n_i\) integer, on the sphere. They use ODE methods and the geometry of Gaussian curvature of so-called HCMU metrics, which are the simplest cases of Calabi's extremal metrics in singular spaces. Moreover, the considered HCMU metrics on \(S^2\) are classified: explicit formulae are given via rational holomorphic functions on \(\mathbb{C}\).
scientific article; zbMATH DE number 1775022