Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification
We give a geometric condition on a meromorphic affine connection for its Killing vector fields to be single-valued. More precisely, this condition relies on the pole of the connection and its geodesics, and defines a subcategory. To this end, we use the equivalence between these objects and meromorp...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211979 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification. Alexis Garcia. SIGMA 19 (2023), 052, 35 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We give a geometric condition on a meromorphic affine connection for its Killing vector fields to be single-valued. More precisely, this condition relies on the pole of the connection and its geodesics, and defines a subcategory. To this end, we use the equivalence between these objects and meromorphic affine Cartan geometries. The proof of the previous result is then a consequence of a more general result linking the distinguished curves of meromorphic Cartan geometries, their poles, and their infinitesimal automorphisms, which is the main purpose of the paper. This enables extending the classification result from [Biswas I., Dumitrescu S., McKay B., Épijournal Géom. Algébrique 3 (2019), 19, 10 pages, arXiv:1804.08949] to the subcategory of meromorphic affine connection described before.
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| ISSN: | 1815-0659 |