The Gauss-Bonnet Theorem for Vector Bundles
نویسنده
چکیده
We 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. Mathematics Subject Classification (2000): 58A10, 53C05, 57R20.
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