A characterization of chains in dimension three

2023/03/15 by Wojciech Kryński, Kryński, Wojciech, Omid Makhmali +1
Mathematics · #32V99 #34A26 #34A55 #53A55 #53B15 #53C15 #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Point processes and geometric inequalities #Primary: 53A40 #Secondary: 53A20

paper · pdf · doi:10.48550/arxiv.2303.08807

openalex publication_date 2023/03/15 · openalex created_date 2023/03/18 · openalex updated_date 2026/07/28

Abstract

Given a 3-dimensional (para-)CR structure, its family of chains define a 3-dimensional path geometry. We provide necessary and sufficient conditions that determine whether a path geometry in dimension three arises from chains of a CR or para-CR 3-manifold. We demonstrate how our characterization can be verified computationally for a given 3-dimensional path geometry and discuss a few examples.

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