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: Garcia, Alexis
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2023
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

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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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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