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| HAL : hal-00702324, version 1 |
| arXiv : 1205.6562 |
| Fiche détaillée |  Récupérer au format |
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| Linear differential operators on contact manifolds |
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| Charles H. Conley 1Valentin Ovsienko 2 |
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| (30/05/2012) |
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| We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg calculus: noncommutative symbolic calculus, the principal symbol, and the contact order to such differential operators. Our first main result is an intrinsically defined ''subsymbol'' of a differential operator, which is a differential invariant of degree one lower than that of the principal symbol. In particular, this subsymbol associates a contact vector field to an arbitrary second order linear differential operator. Our second main result is the construction of a filtration that strengthens the well-known contact order filtration of the Heisenberg calculus. |
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| 1 : | Department of Mathematics Univ. North Texas |
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University of North Texas |
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| 2 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| Domaine | : | Mathématiques/Physique mathématique Mathématiques/Géométrie différentielle Mathématiques/Théorie des représentations |
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| Contact geometry – differential operators – Heisenberg calculus – infinitesimal characters – differential invariants |
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| hal-00702324, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00702324 | |
| oai:hal.archives-ouvertes.fr:hal-00702324 | |
| Contributeur : Valentin Ovsienko | |
| Soumis le : Mercredi 30 Mai 2012, 05:46:51 | |
| Dernière modification le : Mercredi 30 Mai 2012, 09:23:34 | |
