Local Integrability of Mizohata Structures

In this work we study the local integrability of strongly pseudoconvex Mizohata structures of frank$n > 2$(and co-rank 1). These structures are locally generated in an appropriate coordinate system (t1, ..., tn, x) by flat perturbations of Mizohata vector fields Mj= ∂/∂ tj- itj∂/∂ x, j = 1, ...,...

Full description

Saved in:
Bibliographic Details
Published in:Transactions of the American Mathematical Society 1993, Vol.338 (1), p.337-362
Main Authors: Hounie, Jorge, Malagutti, Pedro
Format: Article
Language:English
Subjects:
Adzes
Coordinate systems
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical functions
Mathematical manifolds
Mathematical theorems
Mathematics
Nonexistence
Sciences and techniques of general use
Solvability
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Vector fields
Zoos
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this work we study the local integrability of strongly pseudoconvex Mizohata structures of frank$n > 2$(and co-rank 1). These structures are locally generated in an appropriate coordinate system (t1, ..., tn, x) by flat perturbations of Mizohata vector fields Mj= ∂/∂ tj- itj∂/∂ x, j = 1, ..., n. For this, we first prove the global integrability of small perturbations of the structure generated by$\frac{\partial}{\partial \overline z} + \sigma_1\frac{\partial}{\partial z}, \frac{\partial}{\partial\theta_{n - 1}} + \sigma_j\frac{\partial}{\partial z}, j = 2, \ldots, n$, defined over a manifold C × S, where S is simply connected.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-1993-1106189-4