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Bibliographic Details
Main Author: Simić, Slobodan N.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2403.17150
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author Simić, Slobodan N.
author_facet Simić, Slobodan N.
contents We generalize the classical Frobenius integrability theorem to plane fields of class $C^Q$, a regularity class introduced by Reimann [Rei76] for vector fields in Euclidean spaces. A $C^Q$ vector field is uniquely integrable and its flow is a quasiconformal deformation. We show that an a.e. involutive $C^Q$ plane field (defined in a suitable way) in $\mathbb{R}^n$ is integrable, with integral manifolds of class $C^1$.
format Preprint
id arxiv_https___arxiv_org_abs_2403_17150
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Frobenius integrability theorem for plane fields generated by quasiconformal deformations
Simić, Slobodan N.
Differential Geometry
58A30, 34A34, 57R25
We generalize the classical Frobenius integrability theorem to plane fields of class $C^Q$, a regularity class introduced by Reimann [Rei76] for vector fields in Euclidean spaces. A $C^Q$ vector field is uniquely integrable and its flow is a quasiconformal deformation. We show that an a.e. involutive $C^Q$ plane field (defined in a suitable way) in $\mathbb{R}^n$ is integrable, with integral manifolds of class $C^1$.
title A Frobenius integrability theorem for plane fields generated by quasiconformal deformations
topic Differential Geometry
58A30, 34A34, 57R25
url https://arxiv.org/abs/2403.17150