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...
Збережено в:
| Опубліковано в: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| ISSN: | 1815-0659 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | 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 |
| Цитувати: | Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations. Vicente Cortés and Thomas Leistner. SIGMA 20 (2024), 084, 12 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 |