The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three - Marugame, Taiji (Symmetry, Integrability and Geometry: Methods and Applications, 2025)
We give an explicit description of the Fefferman metric for twistor CR manifolds in terms of Riemannian structures on the base conformal 3-manifolds. As an application, we prove that chains and null chains on twistor CR manifolds project to conformal geodesics, and that any conformal geodesic has lifts both to a chain and a null chain. By using this correspondence, we give a variational characterization of conformal geodesics in dimension three, which involves the total torsion functional.