Contact manifolds, Lagrangian Grassmannians and PDEs

In 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...

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Autores principales:	Eshkobilov Olimjon, Manno Gianni, Moreno Giovanni, Sagerschnig Katja
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2018
Materias:	contact and symplectic manifolds jet spaces lagrangian grassmannians first and second order pdes symmetries of pdes characteristics monge-ampère equations pdes on complex manifolds 32c15 35a30 35k96 53c30 53c55 53d05 53d10 58a20 58a30 58j70 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/7f242cfb7a274a588821b475eb6cb7c1
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id	oai:doaj.org-article:7f242cfb7a274a588821b475eb6cb7c1
record_format	dspace
spelling	oai:doaj.org-article:7f242cfb7a274a588821b475eb6cb7c12021-12-02T16:36:59ZContact manifolds, Lagrangian Grassmannians and PDEs2300-744310.1515/coma-2018-0003https://doaj.org/article/7f242cfb7a274a588821b475eb6cb7c12018-02-01T00:00:00Zhttps://doi.org/10.1515/coma-2018-0003https://doaj.org/toc/2300-7443In 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.Eshkobilov OlimjonManno GianniMoreno GiovanniSagerschnig KatjaDe Gruyterarticlecontact and symplectic manifoldsjet spaceslagrangian grassmanniansfirst and second order pdessymmetries of pdescharacteristicsmonge-ampère equationspdes on complex manifolds32c1535a3035k9653c3053c5553d0553d1058a2058a3058j70MathematicsQA1-939ENComplex Manifolds, Vol 5, Iss 1, Pp 26-88 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	contact and symplectic manifolds jet spaces lagrangian grassmannians first and second order pdes symmetries of pdes characteristics monge-ampère equations pdes on complex manifolds 32c15 35a30 35k96 53c30 53c55 53d05 53d10 58a20 58a30 58j70 Mathematics QA1-939
spellingShingle	contact and symplectic manifolds jet spaces lagrangian grassmannians first and second order pdes symmetries of pdes characteristics monge-ampère equations pdes on complex manifolds 32c15 35a30 35k96 53c30 53c55 53d05 53d10 58a20 58a30 58j70 Mathematics QA1-939 Eshkobilov Olimjon Manno Gianni Moreno Giovanni Sagerschnig Katja Contact manifolds, Lagrangian Grassmannians and PDEs
description	In 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.
format	article
author	Eshkobilov Olimjon Manno Gianni Moreno Giovanni Sagerschnig Katja
author_facet	Eshkobilov Olimjon Manno Gianni Moreno Giovanni Sagerschnig Katja
author_sort	Eshkobilov Olimjon
title	Contact manifolds, Lagrangian Grassmannians and PDEs
title_short	Contact manifolds, Lagrangian Grassmannians and PDEs
title_full	Contact manifolds, Lagrangian Grassmannians and PDEs
title_fullStr	Contact manifolds, Lagrangian Grassmannians and PDEs
title_full_unstemmed	Contact manifolds, Lagrangian Grassmannians and PDEs
title_sort	contact manifolds, lagrangian grassmannians and pdes
publisher	De Gruyter
publishDate	2018
url	https://doaj.org/article/7f242cfb7a274a588821b475eb6cb7c1
work_keys_str_mv	AT eshkobilovolimjon contactmanifoldslagrangiangrassmanniansandpdes AT mannogianni contactmanifoldslagrangiangrassmanniansandpdes AT morenogiovanni contactmanifoldslagrangiangrassmanniansandpdes AT sagerschnigkatja contactmanifoldslagrangiangrassmanniansandpdes
_version_	1718383641787105280

Contact manifolds, Lagrangian Grassmannians and PDEs

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