A proof of Gauss-Bonnet theorem - Local version

DOI: 10.18173/2354-1059.2021-0001

Abstract

We present a short proof with details for the local Gauss-Bonnet theorem, a deep result in differential geometry, which shows a connection between differential geometric and topological aspects. However, this theorem is left to students according to the new programme in our faculty. The main idea in the proof makes use of Stokes’ theorem.