2 edition of **Local integrability of Mizohata structures** found in the catalog.

Local integrability of Mizohata structures

Jorge Hounie

- 158 Want to read
- 19 Currently reading

Published
**1990**
by Universidade Federal de Pernambuco, Centro de Ciências Exatas e da Natureza, Departamento de Matemática in Recife, Brasil
.

Written in English

- Vector fields.,
- Homotopy theory.

**Edition Notes**

Includes bibliographical references (p. 31).

Other titles | Mizohata structures. |

Statement | by Jorge Hounie and Pedro Malagutti. |

Series | Notas e comunicações de matemática ;, no. 171 |

Contributions | Malagutti, Pedro. |

Classifications | |
---|---|

LC Classifications | QA1 .N863 no. 171, QA613.619 .N863 no. 171 |

The Physical Object | |

Pagination | 31 p. ; |

Number of Pages | 31 |

ID Numbers | |

Open Library | OL1281728M |

LC Control Number | 92139015 |

Request PDF | An Introduction to Involutive Structure | Detailing the main methods in the theory of involutive systems of complex vector fields this book examines the major results from the last. integrability, or rather of local integrability, which is the assertion of the existence of "enough" local solutions to the homogeneous equations (1). Before discussing the latter concept let us give a brief list of important special classes of formally integrable structures (this refers to vector bundles like r .

This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors. It is written in an accessible and informal style, and fills a gap in the existing. THE MIZOHATA COMPLEX One of the main results of this paper (theorem ) is that for q > 2, (10) Hq Hql(Skl x Snki) 0 S if In - 2kl n; H,q Hql (Sn-l) o& S if In - 2kl n, where w is the germ of a Mizohata structure with signature In - 2kl, Sm is the m sphere, H* (M) is the De-Rham cohomology of the manifold M, and where s = Hd(x+iy) (To.

There are other books which cover particular topics treated in the course: • Integrability of ODEs [4] (Hamiltonian formalism, Arnold–Liouville theorem, action– angle variables). The integrability of ordinary diﬀerential equations is a fairly clear con-cept (i.e. it can be deﬁned) based on existence of suﬃciently many well behaved. 4. The aberrant case. In this section we will show that when V is a local Mizohata structure (i.e. n = 0, d = 1 and Levi form nondegenerate) of aberrant signature, then it is possible that V may possess no integrals. This result is due to [T3]. Here we provide a different proof.

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LOCAL INTEGRABILITY OF MIZOHATA STRUCTURES JORGE HOUNIE AND PEDRO MALAGUTTI Abstract. In this work we study the local integrability of strongly pseudocon-vex Mizohata structures of rank n Local integrability of Mizohata structures book 2 (and co-rank 1).

These structures are locally generated in an appropriate coordinate system (t\,tn, x) by flat. Abstract: In this work we study the local integrability of strongly pseudoconvex Mizohata structures of rank (and co-rank).

These structures are locally generated in an appropriate coordinate system by flat perturbations of Mizohata vector fields. This paper deals with the integrability problem for structures on the sphere S2 which are elliptic on the upper and lower hemispheres, and which are given by a simple fold on the equator.

Criteria for standardness are given. Existence and factorization of first integrals are by: 1. Abstract. In this thesis we study the relation between CR-structures on three-dimensional manifolds and Mizohata structures on two-dimensional manifolds.^ Let $(X, H\sp{0,1})$ be a three-dimensional strictly pseudoconvex : Anbo Le.

The Mizohata partial differential operator is generalized to global structures on compact two-dimensional manifolds. A generalization of the Hopf Theorem on vector fields is used to show that a first integral can exist if and only if the genus is even.

The Mizohata structures on the sphere are classified by the diffeomorphism group of the circle modulo the Moebius subgroup and a necessary Cited by: The main result of this paper establishes the rigidity of pseudoconvex Mizohata structures on compact manifolds with abelian fundamental groups.

Any simply connected \((n+1)\)-dimensional compact manifold with a pseudoconvex Mizohata structure is equivalent the standard Mizohata structure on the sphere \(\mathbb {S}^{n+1}\).

In connection with the question of local integrability of strongly pseudoconvex involutive structures of co-rank one, we prove existence and nonexistence of homotopy formulas on 1-forms for the Mizohata structure in ℝn+1 and relate them to local integrability.

Local generators in analytic structures 25 Integrability of complex and elliptic structures 26 Elliptic structures in the real plane 28 Compatible submanifolds Locally integrable CR structures - 36 A CR structure that is not locally integrable 38 The Levi form on a formally ihtegrable structure Abstract.

Necessary and sufficient conditions for the local integrability of systems of m linearly independent smooth complex vector fields defined on m +1 dimensional smooth real manifolds are given.

Some similar results for the closely related abstract CR structures of. VII Local solvability versus local integrability Notes 2 Mizohata structures 3 Hypoanalytic structures This book introduces the reader to a number of results on systems of vector fields with complex-valued coefficients defined on a smooth manifold.

Baouendi and F. Trèves, A local constancy principle for the solutions of certain overdetermined systems of first-order linear partial differential equations, Adv.

in Stud., vol. 7, Academic Press, New York-London,pp. – MR Paulo Cordaro and Jorge Hounie, On local solvability of underdetermined systems of vector fields, Amer.

Math. (), no. Baouendi and F. Trèves, A local constancy principle for the solutions of certain overdetermined systems of first-order linear partial differential equations, Adv.

in Math. Suppl. Stud., vol. 7, Academic Press, New York-London,pp. – MR We will call S-geometrical structures which are solutions of a natural equation Y ⊂ J k π, π being the natural bundle of S-geometrical structures on M, as Y-special. For instance, foliations are Y-special distributions where Y is the natural equation from the first of the examples above.

If s: M → E is a Y-special structure on M the image of its characteristic map ζ(s): M → Ch (S. The integrability of deformations condition of CR structures Masatake Kuranishi Columbia University Introduction The parameterization of deformations of a complex manifold by type (1, 0)-valued differential forms of type (0, 1) and the representation of the integrability condition by differential equations on the forms were the keys to open the way to apply the theory of elliptic partial.

The Lewy operator and the Mizohata operator are much more similar than it may look. Indeed, they are micro-locally equivalent (, Sect. 9, Chap. IX), and in fact they serve as micro-local model for non-Levi degenerate CR-structures.

Perturbations of the Lewy operator and of the Mizohata operator are of interest. See, Chap. We prove that a nondegenerate CR structure with signature (p;n−p)at02R2n+1 and with n rst integrals z1; ;znsatisfying dz1 ^dz 1 ^^dzn^dz n6=0 is realizable if and only if an action of the groupO(2p;2n−2p) leaves invariant a one-dimensional subbundle of the structure bundle.

1 The local realizability (embeddability) of CR structures has been. Book. Jan ; Heinz Bauer; In this work we study the local integrability of strongly pseudocon-vex Mizohata structures of rank n > 2 (and co-rank 1).

The following conditions are equivalent: (i) is a Mizohata structure, (ii) For every peZ one of the following alternatives holds: either (a) the signature of at p is {0, n} or (b) the signature of 'is not {O,M} and for every function Z; defined in a small neighborhood U of p and satisfying ILZ) = 0, the set Zi((7nZ') is a real analytic curve ofC.

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In connection with the question of local integrability of strongly pseudoconvex involutive structures of co-rank one, we prove existence and nonexistence of homotopy formulas on 1-forms for the.

We observe that the operator L given in () belongs to our class X. Notice that, in this case, is the line (=0 and that local integrability follows outside S by ellipticity and on E because L is the Mizohata operator in a neighborhood of E, THEOREM The local solvability of systems of partial differential equations is studied in some detail.

The book provides a solid background for others new to the field and also contains a treatment of many recent results which will be of interest to researchers in the subject.In this thesis we study the relation between CR-structures on three-dimensional manifolds and Mizohata structures on two-dimensional manifolds.

Conversely, the local integrability of the.