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Integral of the Pfaffian form of a dual \(g\)-metric connection. (Intégrale de la forme pfaffienne d’une connexion duale \(g\)-métrique.) (French) Zbl 0653.58005

Summary: Gauss-Bonnet’s theorem says that the integral of the Pfaffian form of a metric connection on a compact manifold is equal to the Euler-Poincaré characteristic of this manifold. In singular situations, the integral of the Pfaffian form is generally divergent. The purpose of this note is to give an asymptotic expression of this integral when the singular set of the pseudo-metric is a submanifold of codimension one.

MSC:

58C35 Integration on manifolds; measures on manifolds
58A17 Pfaffian systems
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