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arXiv · 2411.18961

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

Taiji Marugame
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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.

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Taiji Marugame. 2024-11-28. The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three. https://doi.org/10.3842/sigma.2025.090

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