A Frobenius integrability theorem for plane fields generated by quasiconformal deformations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917624367022080 |
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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 |