Holomorphic vector fields with real integral manifolds
Complex Variables
2024-08-12 v1 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.2408.05186,
title = {Holomorphic vector fields with real integral manifolds},
author = {Martin Kolář and Ilya Kossovskiy and Bernhard Lamel},
journal= {arXiv preprint arXiv:2408.05186},
year = {2024}
}