A contact distribution C on a manifold M determines a symplectic bundle C → M. In this paper we find normal forms for its lagrangian distributions by classifying vector fields lying in C. Such vector fields are divided into three types and described in terms of the simplest ones (characteristic fields of 1st order PDE's). After having established the equivalence between parabolic Monge-Ampère equations (MAE's) and lagrangian distributions in terms of characteristics, as an application of our results we give normal forms for parabolic MAE's. © 2008 Elsevier B.V. All rights reserved.

Alonso Blanco, R., Manno, G., Pugliese, F. (2009). Normal forms for lagrangian distributions on 5-dimensional contact manifolds. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 27(2), 212-229 [10.1016/j.difgeo.2008.06.019].

Normal forms for lagrangian distributions on 5-dimensional contact manifolds

MANNO, GIOVANNI;
2009

Abstract

A contact distribution C on a manifold M determines a symplectic bundle C → M. In this paper we find normal forms for its lagrangian distributions by classifying vector fields lying in C. Such vector fields are divided into three types and described in terms of the simplest ones (characteristic fields of 1st order PDE's). After having established the equivalence between parabolic Monge-Ampère equations (MAE's) and lagrangian distributions in terms of characteristics, as an application of our results we give normal forms for parabolic MAE's. © 2008 Elsevier B.V. All rights reserved.
Articolo in rivista - Articolo scientifico
contact manifolds, lagrangian distributions, characteristics of second order PDE's, parabolic Monge-Ampere equations
English
212
229
Alonso Blanco, R., Manno, G., Pugliese, F. (2009). Normal forms for lagrangian distributions on 5-dimensional contact manifolds. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 27(2), 212-229 [10.1016/j.difgeo.2008.06.019].
Alonso Blanco, R; Manno, G; Pugliese, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/5293
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