HOLOMORPHIC VECTOR FIELDS WITH A BARYCENTRIC CONDITION

Dominique Cerveau; Julie Déserti; Alcides Lins Neto

doi:10.5565/PUBLMAT6812413

2024 HOLOMORPHIC VECTOR FIELDS WITH A BARYCENTRIC CONDITION

Dominique Cerveau, Julie Déserti, Alcides Lins Neto

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Abstract

We study the $p$ -tuples of holomorphic vector fields $(X_1,X_2,\dotsc,X_p)$ satisfying the barycentric property $\sum\limits_k\exp tX_k=p\cdot\operatorname{id}$ , where $\exp tX$ denotes the flow of $X$ .

Funding Statement

Cerveau is supported by CNRS and Lebesgue center, program ANR-11-LABX-0020-0. A. Lins Neto is partially supported by CNPq and Université de Rennes 1.

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Dominique Cerveau. Julie Déserti. Alcides Lins Neto. "HOLOMORPHIC VECTOR FIELDS WITH A BARYCENTRIC CONDITION." Publ. Mat. 68 (1) 287 - 330, 2024. https://doi.org/10.5565/PUBLMAT6812413

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Received: 1 September 2022; Accepted: 15 May 2023; Published: 2024

First available in Project Euclid: 25 December 2023

MathSciNet: MR4682733

Digital Object Identifier: 10.5565/PUBLMAT6812413

Subjects:

Primary: 32A10‎ , 32M35 , 34M45

Keywords: barycentric property , Differential equation , flow , vector fields

Abstract

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