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High-order angles in almost-Riemannian geometry

Show simple item record Boscain, Ugo en_US Sigalotti, Mario en_US 2007-08-24T12:00:46Z en_US 2011-09-07T20:26:25Z 2007-08-24T12:00:46Z en_US 2011-09-07T20:26:25Z 2007-08-24T12:00:46Z en_US
dc.identifier.uri en_US
dc.description.abstract Let X and Y be two smooth vector fields on a two-dimensional manifold M. If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula for domains with piecewise-C2 boundary. The main feature of such formula is the presence of terms that play the role of high-order angles at the intersection points with the set of singularities. en_US
dc.format.extent 168685 bytes en_US
dc.format.mimetype application/pdf en_US
dc.language.iso en_US en_US
dc.relation.ispartofseries SISSA;59/2007/M en_US
dc.title High-order angles in almost-Riemannian geometry en_US
dc.type Preprint en_US
dc.contributor.department Functional Analysis and Applications en_US
dc.contributor.area Mathematics en_US

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