The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three

Taiji Marugame

Department of Mathematics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan

Abstract: 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.

Keywords: twistor CR manifold, Fefferman metric, conformal geodesic.

MSC: 53B20, 32V05, 53C18

Received: June 3, 2025; in final form October 16, 2025; Published online October 24, 2025

Language: English

DOI: 10.3842/SIGMA.2025.090

ArXiv: 2411.18961