A characterization of chains in dimension three
arXiv:2303.08807
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.
23 pages; final version; minor corrections are made; Section 4 in the previous version is removed and will be extended into a separate article titled "Lewy curves in para-CR geometry"; To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)