Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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O. Eshkobilov - G. Manno - G. Moreno - K. Sagerschnig

Contact manifolds, Lagrangian Grassmannians and PDEs

created by moreno on 07 Feb 2018
modified on 15 Sep 2020



Inserted: 7 feb 2018
Last Updated: 15 sep 2020

Journal: Complex Manifolds
Volume: 5
Number: 1
Pages: 26-88
Year: 2018
Doi: 10.1515/coma-2018-0003

ArXiv: 1708.02718 PDF
Links: PDF


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 30-hours Ph.D course given by two of the authors (GM and GM). 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.


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