The Gauss-Bonnet formula of a conical metric on a compact Riemann surface
Differential Geometry
2023-04-25 v3
Abstract
We prove a generalization of the classical Gauss-Bonnet formula for a conical metric on a compact Riemann surface provided that the Gaussian curvature is Lebesgue integrable with respect to the area form of the metric. We also construct explicitly some conical metrics whose curvature is not integrable.
Keywords
Cite
@article{arxiv.1912.01187,
title = {The Gauss-Bonnet formula of a conical metric on a compact Riemann surface},
author = {Hanbing Fang and Bin Xu and Bairui Yang},
journal= {arXiv preprint arXiv:1912.01187},
year = {2023}
}
Comments
5 pages, 0 figures; final version