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arXiv · 1708.02718

Contact manifolds, Lagrangian Grassmannians and PDEs

Olimjon Eshkobilov·Gianni Manno·Giovanni Moreno·Katja Sagerschnig
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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.

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Olimjon Eshkobilov, Gianni Manno, Giovanni Moreno, Katja Sagerschnig. 2017-08-09. Contact manifolds, Lagrangian Grassmannians and PDEs. https://arxiv.org/abs/1708.02718

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