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 with two conical singularities, which was first proved by Troyanov in \cite{Tr89} by using projective connection.
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