English

Two families of reducible spherical conical metrics

Differential Geometry 2025-11-25 v2

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.

Keywords

Cite

@article{arxiv.2511.15598,
  title  = {Two families of reducible spherical conical metrics},
  author = {Haoran Wu and Xuwen Zhu},
  journal= {arXiv preprint arXiv:2511.15598},
  year   = {2025}
}

Comments

The statement of Theorem 1.3 and the bibliography have been updated