Geometry and dynamics of Engel structures
Yoshihiko Mitsumatsu
TL;DR
This paper advances the understanding of Engel structures by developing canonical geometric constructions and analyzing the dynamics of Cauchy characteristics, revealing their elliptic, parabolic, or hyperbolic behaviors.
Contribution
It introduces new geometric constructions and analyzes the dynamics of Cauchy characteristics within Engel structures, highlighting their diverse natures.
Findings
Canonical geometric constructions for Engel structures
Dynamics of Cauchy characteristics vary in elliptic, parabolic, hyperbolic cases
Enhanced understanding of Engel structures' geometric and dynamic properties
Abstract
The aim of this paper is to extend basic understanding of Engel structures through developing geometric constructions which are canonical to a certain degree and the dynamics of Cauchy characteristics in the transverse spaces which may exhibit elliptic, parabolic, or hyperbolic natures in typical cases.
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Taxonomy
TopicsGeometric and Algebraic Topology · Nonlinear Waves and Solitons · Geometry and complex manifolds