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| _version_ | 1862680986632847360 |
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| author | Marugame, Taiji |
| author_facet | Marugame, Taiji |
| citation_txt | The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three. Taiji Marugame. SIGMA 21 (2025), 090, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-17T00:19:06Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214194 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T00:19:06Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Marugame, Taiji 2026-02-20T08:00:29Z 2025 The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three. Taiji Marugame. SIGMA 21 (2025), 090, 26 pages 1815-0659 2020 Mathematics Subject Classification: 53B20; 32V05; 53C18 arXiv:2411.18961 https://nasplib.isofts.kiev.ua/handle/123456789/214194 https://doi.org/10.3842/SIGMA.2025.090 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. The author thanks the anonymous referees for their comments. This work was partially supported by JSPS KAKENHI Grant Number 22K13922. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three Article published earlier |
| spellingShingle | The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three Marugame, Taiji |
| title | The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three |
| title_full | The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three |
| title_fullStr | The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three |
| title_full_unstemmed | The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three |
| title_short | The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three |
| title_sort | fefferman metric for twistor cr manifolds and conformal geodesics in dimension three |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214194 |
| work_keys_str_mv | AT marugametaiji thefeffermanmetricfortwistorcrmanifoldsandconformalgeodesicsindimensionthree AT marugametaiji feffermanmetricfortwistorcrmanifoldsandconformalgeodesicsindimensionthree |