Parallel Translation in Vector Bundles with Abelian Structure Group and the Gauss-Bonnet Formula
Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 765-771
Voir la notice de l'article provenant de la source Cambridge University Press
Most proofs for the classical Gauss-Bonnet formula use special coordinates, or other non-trivial preparations. Here, a simple proof is given, based on the fact that the structure group SO(2) of the tangent bundle of an oriented 2-dimensional Riemannian manifold is abelian. Since only this hypothesis is used, we prove a slightly more general result (Theorem 1).
Rummler, Hansklaus. Parallel Translation in Vector Bundles with Abelian Structure Group and the Gauss-Bonnet Formula. Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 765-771. doi: 10.4153/CJM-1973-078-9
@article{10_4153_CJM_1973_078_9,
author = {Rummler, Hansklaus},
title = {Parallel {Translation} in {Vector} {Bundles} with {Abelian} {Structure} {Group} and the {Gauss-Bonnet} {Formula}},
journal = {Canadian journal of mathematics},
pages = {765--771},
year = {1973},
volume = {25},
number = {4},
doi = {10.4153/CJM-1973-078-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1973-078-9/}
}
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