Two families of reducible spherical conical metrics

2025/11/19 by Wu, Haoran, Zhu, Xuwen
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2511.15598

Abstract

We analyze a 1-parameter family of heart shape and a 3-parameter family obtained by gluing three footballs, both of which are examples of reducible spherical conical metrics. For these examples we verify the structure theorem given in [15] and show that such metrics naturally arise from Abelian differentials of the third kind. We then obtain the geometric decomposition using explicit metric and geodesic calculations. This offers new evidence for the interaction between the synthetic spherical geometry and the complex analytic structure of reducible conical metrics.

Citations

• Finite isoresidual covers in strata of k-differentials
• Geometric structure and existence of reducible spherical conical metrics
• Dihedral monodromy of cone spherical metrics
• Spherical conical metrics and harmonic maps to spheres
• Geometric decompositions of surfaces with spherical metric and conical\n singularities
• Metrics of constant curvature 1 with three conical singularities on 2-sphere

Related

• Geometric structure and existence of reducible spherical conical metrics
• Even Cone Spherical Metrics: Blow-Up at a Cone Singularity
• On circle patterns and spherical conical metrics
• Existence and non-uniqueness of cone spherical metrics with prescribed singularities on a compact Riemann surface with positive genus
• Geometric decompositions of surfaces with spherical metric and conical\n singularities