The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three
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 li...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/214194 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three. Taiji Marugame. SIGMA 21 (2025), 090, 26 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |