Flat sub-Lorentzian structures on Martinet distribution
Yu. L. Sachkov
TL;DR
This paper investigates two flat sub-Lorentzian control problems on the Martinet distribution, analyzing their attainable sets, optimal trajectories, and distances, revealing differences in their geometric properties.
Contribution
It provides a detailed geometric analysis of two specific flat sub-Lorentzian problems on the Martinet distribution, highlighting differences in their attainable sets.
Findings
The first problem's attainable set intersects the Martinet plane.
The second problem's attainable set does not intersect the Martinet plane.
Explicit descriptions of optimal trajectories and sub-Lorentzian distances.
Abstract
Two flat sub-Lorentzian problems on the Martinet distribution are studied. For the first one, the attainable set has a nontrivial intersection with the Martinet plane, but for the second one it does not. Attainable sets, optimal trajectories, sub-Lorentzian distances and spheres are described.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Ophthalmology and Eye Disorders