×

zbMATH — the first resource for mathematics

On the Gauss-Bonnet theorem for singular pseudo-metrics. (Sur le théorème de Gauss-Bonnet pour les pseudo-métriques singuliéres.) (French) Zbl 1149.53314
Séminaire de théorie spectrale et géométrie. Année 1986-1987. Chambéry: Univ. de Savoie, Fac. des Sciences, Service de Mathématiques; St. Martin d’Hères: Univ. de Grenoble I, Inst. Fourier. Sémin. Théor. Spectrale Géom., Chambéry-Grenoble 5, 99-105 (1987).
Summary: A pseudo-metric \(g\) is a field of symmetric bilinear forms on a manifold \(M\). If \(g\) is nondegenerate and \(M\) compact, then the classical theorem of Chern-Gauss-Bonnet affirms that the integral of the Pfaffian of a metric compatible with \(g\) is equal to the Euler class of \(M\). This property is no longer true, in general, if \(g\) is degenerate. The object of this article is to study such a situation when the singular locus of \(g\), that is the set of points of \(M\) where \(g\) is degenerate, is a submanifold of codimension 1.
For the entire collection see [Zbl 0825.00040].

MSC:
53C35 Differential geometry of symmetric spaces
58A17 Pfaffian systems
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C40 Global submanifolds
PDF BibTeX XML Cite
Full Text: EuDML