The Gauss-Bonnet theorem for vector bundles

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dc.creatorBell, Denis
dc.date2007-02-06
dc.date.accessioned2026-07-07T07:45:18Z
dc.date.available2026-07-07T07:45:18Z
dc.descriptionWe give a short proof of the Gauss-Bonnet theorem for a real oriented Riemannian vector bundle $E$ of even rank over a closed compact orientable manifold $M$. This theorem reduces to the classical Gauss-Bonnet-Chern theorem in the special case when $M$ is a Riemannian manifold and $E$ is the tangent bundle of $M$ endowed with the Levi-Civita connection. The proof is based on an explicit geometric construction of the Thom class for 2-plane bundles.
dc.identifierhttps://arxiv.org/abs/math/0702162
dc.identifierhttp://arxiv.org/abs/math/0702162
dc.identifierJournal of Geometry 85, no. 1-2, 15-21, 2006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123490
dc.subjectDifferential Geometry
dc.titleThe Gauss-Bonnet theorem for vector bundles
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