Gauss--Bonnet theorem for compact and orientable surfaces: a proof without using triangulations
Differential Geometry
2020-06-25 v3 Complex Variables
Abstract
The aim of this note is to provide an intrinsic proof of the Gauss--Bonnet theorem without invoking triangulations, which is achieved by exploiting complex structures.
Cite
@article{arxiv.1709.09040,
title = {Gauss--Bonnet theorem for compact and orientable surfaces: a proof without using triangulations},
author = {Romero Solha},
journal= {arXiv preprint arXiv:1709.09040},
year = {2020}
}
Comments
8+4 pages (a 4 pages appendix including a proof of the formula relating the curvatura integra and the genus was added)