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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212611 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| Summary: | 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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| ISSN: | 1815-0659 |