A Frobenius integrability theorem for plane fields generated by quasiconformal deformations
Publication Date
12-1-2024
Document Type
Article
Publication Title
Differential Geometry and its Application
Volume
97
DOI
10.1016/j.difgeo.2024.102202
Abstract
We generalize the classical Frobenius integrability theorem to plane fields of class CQ, a regularity class introduced by Reimann [9] for vector fields in Euclidean spaces. Reimann showed that a CQ vector field is uniquely integrable and its flow is a quasiconformal deformation. We prove that an a.e. involutive CQ plane field (defined in a suitable way) in Rn is integrable, with integral manifolds of class C1,Q.
Funding Sponsor
San José State University
Keywords
Integrability, Plane field, Quasiconformal, Regular Lagrangian flow
Department
Mathematics and Statistics
Recommended Citation
Slobodan N. Simić. "A Frobenius integrability theorem for plane fields generated by quasiconformal deformations" Differential Geometry and its Application (2024). https://doi.org/10.1016/j.difgeo.2024.102202
