Contact manifolds, Lagrangian Grassmannians and PDEs
Differential Geometry
2017-08-31 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1708.02718,
title = {Contact manifolds, Lagrangian Grassmannians and PDEs},
author = {Olimjon Eshkobilov and Gianni Manno and Giovanni Moreno and Katja Sagerschnig},
journal= {arXiv preprint arXiv:1708.02718},
year = {2017}
}
Comments
48 pages, 10 figures