Key points are not available for this paper at this time.
We commonly refer to an extremal K\"ahler metric with finitely many singularities on a compact Riemann surface as an HCMU (Hessian of the Curvature of the Metric is Umbilical) metric. In this study, we specifically classify non-CSC HCMU metrics on the K-surfaces S²\\ and S²\, \.
Meng et al. (Wed,) studied this question.