Dept Math & Stat UiT, Forskningsparken B459

24 May 2023 Wed 10:30-11:30

Omid Makhmali (Warsaw)

"A characterization of chains and dancing paths in dimension three"

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 (para-)CR 3-manifold. Moreover, we invariantly characterize 3-dimensional path geometries arising from another family of canonically defined curves for 3-dimensional para-CR structures, referred to as dancing paths. It turns out that chains and dancing paths coincide only in the case of flat para-CR 3-manifold. Based on a joint work with Wojciech Krynski.