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 |
|---|---|
| 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| _version_ | 1862608146047959040 |
|---|---|
| author | Garcia, Alexis |
| author_facet | Garcia, Alexis |
| citation_txt | Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification. Alexis Garcia. SIGMA 19 (2023), 052, 35 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-14T05:22:36Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211979 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T05:22:36Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Garcia, Alexis 2026-01-20T16:14:01Z 2023 Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification. Alexis Garcia. SIGMA 19 (2023), 052, 35 pages 1815-0659 2020 Mathematics Subject Classification: 53A15; 53B05; 53B15; 53C05; 53C15; 57N16 arXiv:2210.02251 https://nasplib.isofts.kiev.ua/handle/123456789/211979 https://doi.org/10.3842/SIGMA.2023.052 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. We are very grateful to the referees for their helpful work and their constructive comments. We would also like to thank Sorin Dumitrescu for introducing the author to the Cartan geometries. We finally thank the Laboratoire de Mathématiques Blaise Pascal, in Clermont-Ferrand, for its hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification Article published earlier |
| spellingShingle | Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification Garcia, Alexis |
| title | Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification |
| title_full | Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification |
| title_fullStr | Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification |
| title_full_unstemmed | Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification |
| title_short | Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification |
| title_sort | single-valued killing fields of a meromorphic affine connection and classification |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211979 |
| work_keys_str_mv | AT garciaalexis singlevaluedkillingfieldsofameromorphicaffineconnectionandclassification |