Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations
A conformal transformation of a semi-Riemannian manifold is essential if there is no conformally equivalent metric for which it is an isometry. For Riemannian manifolds, the existence of an essential conformal transformation forces the manifold to be conformally flat. This is false for pseudo-Rieman...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212611 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations. Vicente Cortés and Thomas Leistner. SIGMA 20 (2024), 084, 12 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862613247998296064 |
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| author | Cortés, Vicente Leistner, Thomas |
| author_facet | Cortés, Vicente Leistner, Thomas |
| citation_txt | Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations. Vicente Cortés and Thomas Leistner. SIGMA 20 (2024), 084, 12 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A conformal transformation of a semi-Riemannian manifold is essential if there is no conformally equivalent metric for which it is an isometry. For Riemannian manifolds, the existence of an essential conformal transformation forces the manifold to be conformally flat. This is false for pseudo-Riemannian manifolds; however, compact examples of conformally curved manifolds with essential conformal transformation are scarce. Here we give examples of compact conformal manifolds in signature (4 + 2, 4 + 2ℓ) with essential conformal transformations that are locally conformally pseudo-Kähler and not conformally flat, where ≥ 1, , ℓ ≥ 0. The corresponding local pseudo-Kähler metrics obtained by a local conformal rescaling are Ricci-flat.
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| first_indexed | 2026-03-21T11:55:25Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212611 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:55:25Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Cortés, Vicente Leistner, Thomas 2026-02-09T08:06:10Z 2024 Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations. Vicente Cortés and Thomas Leistner. SIGMA 20 (2024), 084, 12 pages 1815-0659 2020 Mathematics Subject Classification: 53C50; 53C35; 53C18; 53C29 arXiv:2309.11184 https://nasplib.isofts.kiev.ua/handle/123456789/212611 https://doi.org/10.3842/SIGMA.2024.084 A conformal transformation of a semi-Riemannian manifold is essential if there is no conformally equivalent metric for which it is an isometry. For Riemannian manifolds, the existence of an essential conformal transformation forces the manifold to be conformally flat. This is false for pseudo-Riemannian manifolds; however, compact examples of conformally curved manifolds with essential conformal transformation are scarce. Here we give examples of compact conformal manifolds in signature (4 + 2, 4 + 2ℓ) with essential conformal transformations that are locally conformally pseudo-Kähler and not conformally flat, where ≥ 1, , ℓ ≥ 0. The corresponding local pseudo-Kähler metrics obtained by a local conformal rescaling are Ricci-flat. This work was supported by the Australian Research Council via the grant DP190102360 and by the German Science Foundation (DFG) under the Research Training Group 1670 “Mathematics inspired by String Theory” and under Germany’s Excellence Strategy– EXC 2121 “Quantum Universe”– 390833306. V.C. is grateful to the University of Adelaide for its hospitality and support. V.C and T.L. thank Australia’s international and residential mathematical research institute, MATRIX, where the work on the paper started and was finalised. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations Article published earlier |
| spellingShingle | Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations Cortés, Vicente Leistner, Thomas |
| title | Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations |
| title_full | Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations |
| title_fullStr | Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations |
| title_full_unstemmed | Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations |
| title_short | Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations |
| title_sort | compact locally conformally pseudo-kähler manifolds with essential conformal transformations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212611 |
| work_keys_str_mv | AT cortesvicente compactlocallyconformallypseudokahlermanifoldswithessentialconformaltransformations AT leistnerthomas compactlocallyconformallypseudokahlermanifoldswithessentialconformaltransformations |