Contact manifolds, Lagrangian Grassmannians and PDEs

Contact manifolds, Lagrangian Grassmannians and PDEs AbstractIn this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n + 1)-dimensional contact manifold and the so-called Lagrangian Grassmannian bundle over the latter. This work is based on a Ph.D course given by two of the authors (G. M. and G. M.). As such, it was mainly designed as a quick introduction to the subject for graduate students. But also the more demanding reader will be gratified, thanks to the frequent references to current research topics and glimpses of higher-level mathematics, found mostly in the last sections. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Complex Manifolds de Gruyter

Contact manifolds, Lagrangian Grassmannians and PDEs

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Publisher
De Gruyter
Copyright
© 2018 Olimjon Eshkobilov, et al., published by De Gruyter
ISSN
2300-7443
eISSN
2300-7443
D.O.I.
10.1515/coma-2018-0003
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n + 1)-dimensional contact manifold and the so-called Lagrangian Grassmannian bundle over the latter. This work is based on a Ph.D course given by two of the authors (G. M. and G. M.). As such, it was mainly designed as a quick introduction to the subject for graduate students. But also the more demanding reader will be gratified, thanks to the frequent references to current research topics and glimpses of higher-level mathematics, found mostly in the last sections.

Journal

Complex Manifoldsde Gruyter

Published: Feb 2, 2018

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