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A characterization of chains in dimension three (2303.08807v3)
Published 15 Mar 2023 in math.DG
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.