Gauss--Bonnet theorem for compact and orientable surfaces: a proof without using triangulations
arXiv:1709.09040
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.
8+4 pages (a 4 pages appendix including a proof of the formula relating the curvatura integra and the genus was added)