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Mathematics > Complex Variables

arXiv:2210.02251 (math)
[Submitted on 5 Oct 2022 (v1), last revised 27 Jul 2023 (this version, v3)]

Title:Single-Valued Killing Fields of a Meromorphic Affine Connection and Classification

Authors:Alexis Garcia
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Abstract: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 to extend the classification result from [Biswas I., Dumitrescu S., McKay B., Épijournal Géom. Algèbrique 3 (2019), 19, 10 pages, arXiv:1804.08949] to the subcategory of meromorphic affine connection described before.
Subjects: Complex Variables (math.CV)
Cite as: arXiv:2210.02251 [math.CV]
  (or arXiv:2210.02251v3 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.2210.02251
Journal reference: SIGMA 19 (2023), 052, 35 pages
Related DOI: https://doi.org/10.3842/SIGMA.2023.052

Submission history

From: Alexis Garcia [view email] [via SIGMA proxy]
[v1] Wed, 5 Oct 2022 13:26:33 UTC (71 KB)
[v2] Tue, 8 Nov 2022 09:20:33 UTC (36 KB)
[v3] Thu, 27 Jul 2023 06:27:57 UTC (43 KB)
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