The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three
Differential Geometry
2025-10-28 v4
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
Cite
@article{arxiv.2411.18961,
title = {The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three},
author = {Taiji Marugame},
journal= {arXiv preprint arXiv:2411.18961},
year = {2025}
}