Abstract
Let π: E→ M be a smooth complex vector bundle of rank k (that is π −1(x) =: E x ≃ℂk) over smooth manifold M equipped with connection ∇. Let R ∇ be the curvature of ∇. As we know, the curvature tensor R = R ∇is related to the connection form ω = (ω ij ) and curvature form Ω = (Ω ij ) as follows Ω ij = dω ij - ω ik Λω kj , for short, Ω = d ω - ωΛω, Ω ij = R hk ij dx h Λdx k . In what follows we will write indices below and we will sum, as usual, over repeating indices.
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© 1997 Springer Science+Business Media Dordrecht
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Maurin, K. (1997). Curvature and Topology or Characteristic Forms of Chern, Pontriagin, and Euler. In: The Riemann Legacy. Mathematics and Its Applications, vol 417. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8939-0_5
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DOI: https://doi.org/10.1007/978-94-015-8939-0_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4876-9
Online ISBN: 978-94-015-8939-0
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