Holomorphic vector fields with real integral manifolds

Fuente: arXiv
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Main Authors: Kolář, Martin, Kossovskiy, Ilya, Lamel, Bernhard
Format: Preprint
Published: 2024
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author Kolář, Martin
Kossovskiy, Ilya
Lamel, Bernhard
author_facet Kolář, Martin
Kossovskiy, Ilya
Lamel, Bernhard
contents We classify singular holomorphic vector fields in two-dimensional complex space admitting a (Levi-nonflat) real-analytic invariant 3-fold through the singularity. In this way, we complete the classification of infinitesimal symmetries of real-analytic Levi-nonflat hypersurfaces in complex two-space. The classification of holomorphic vector fields obtained in the paper has very interesting overlaps with the recent Lombardi-Stolovitch classification theory for holomorphic vector fields at a singularity. In particular, we show that most of the resonances arising in Lombardi-Stolovitch theory do not occur under the presence of (Levi-nonflat) integral manifolds.
format Preprint
id arxiv_https___arxiv_org_abs_2408_05186
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Holomorphic vector fields with real integral manifolds
Kolář, Martin
Kossovskiy, Ilya
Lamel, Bernhard
Complex Variables
Dynamical Systems
32V40, 32H02
We classify singular holomorphic vector fields in two-dimensional complex space admitting a (Levi-nonflat) real-analytic invariant 3-fold through the singularity. In this way, we complete the classification of infinitesimal symmetries of real-analytic Levi-nonflat hypersurfaces in complex two-space. The classification of holomorphic vector fields obtained in the paper has very interesting overlaps with the recent Lombardi-Stolovitch classification theory for holomorphic vector fields at a singularity. In particular, we show that most of the resonances arising in Lombardi-Stolovitch theory do not occur under the presence of (Levi-nonflat) integral manifolds.
title Holomorphic vector fields with real integral manifolds
topic Complex Variables
Dynamical Systems
32V40, 32H02
url https://arxiv.org/abs/2408.05186