English

Constructing constant curvature metrics on Riemann surfaces with singularities

Differential Geometry 2022-04-13 v1

Abstract

By constructing an ODE through a kind of meromorphic 1-forms, we will give an explicit construction of a kind of conformal metrics of constant curvature on Riemann surfaces with singularities. As an application, we will classify constant curvature one metrics on S2S^{2} with two conical singularities, which was first proved by Troyanov in \cite{Tr89} by using projective connection.

Keywords

Cite

@article{arxiv.2204.05565,
  title  = {Constructing constant curvature metrics on Riemann surfaces with singularities},
  author = {Zhiqiang Wei},
  journal= {arXiv preprint arXiv:2204.05565},
  year   = {2022}
}

Comments

8 pages

R2 v1 2026-06-24T10:45:24.911Z