Odd Pfaffian forms
| Autor: | Sergiu Moroianu, Daniel Cibotaru |
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| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Differential Geometry
Riemann curvature tensor Pure mathematics Invariant polynomial General Mathematics Fibration Boundary (topology) Fibered knot Pfaffian Riemannian manifold Volume form symbols.namesake Differential Geometry (math.DG) symbols FOS: Mathematics Mathematics::Differential Geometry 58A10 53C05 (Primary) 57R18 (Secondary) Mathematics::Symplectic Geometry Mathematics |
| DOI: | 10.48550/arxiv.1807.00239 |
| Popis: | On any odd-dimensional oriented Riemannian manifold we define a volume form, which we call the odd Pfaffian, through a certain invariant polynomial with integral coefficients in the curvature tensor. We prove an intrinsic Chern-Gauss-Bonnet formula for incomplete edge singularities in terms of the odd Pfaffian on the fibers of the boundary fibration. The formula holds for product-type model edge metrics where the degeneration is of conical type in each fiber, but also for general classes of perturbations of the model metrics. The same method produces a Chern- Gauss-Bonnet formula for complete, non-compact manifolds with fibered boundaries in the sense of Mazzeo-Melrose and perturbations thereof, involving the odd Pfaffian of the base of the fibration. We deduce the rationality of the usual Pfaffian form on Riemannian orbifolds, and exhibit obstructions for certain metrics on a fibration to be realized as the model at infinity of a flat metric with conical, edge or fibered boundary singularities. Comment: This second version corrects a statement about the degenerate metric on the blow-up of a submanifold, a few typos and includes new references |
| Databáze: | OpenAIRE |
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