English

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.

Keywords

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)

R2 v1 2026-06-22T21:55:21.301Z