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Parallel Translation in Vector Bundles with Abelian Structure Group and the Gauss-Bonnet Formula

Published online by Cambridge University Press:  20 November 2018

Hansklaus Rummler
Hansklaus Rummler*
Affiliation:
Universite de Fribourg, Fribourg, Switzerland
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 765 - 771
Copyright
Copyright © Canadian Mathematical Society 1973

References

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