Exceptionally simple PDE

Dennis The

doi:10.1016/j.difgeo.2017.10.005

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arXiv · 1603.08251

Exceptionally simple PDE

Dennis The

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Abstract

We give local descriptions of parabolic contact structures and show how their flat models yield explicit PDE having symmetry algebras isomorphic to all complex simple Lie algebras except $\mathfrak{sl}_2$. This yields a remarkably uniform generalization of the Cartan-Engel models from 1893 in the $G_2$ case. We give a formula for the harmonic curvature of a $G_2$-contact structure and describe submaximally symmetric models for general $G$-contact structures.

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Dennis The. 2016-03-27. Exceptionally simple PDE. https://doi.org/10.1016/j.difgeo.2017.10.005

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