Introduction to the Geometry of Foliations, Part A

Introduction to the Geometry of Foliations, Part A

Author: Gilbert Hector

Publisher: Springer Science & Business Media

ISBN: 9783322901156

Category: Mathematics

Page: 236

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Foliation theory grew out of the theory of dynamical systems on manifolds and Ch. Ehresmann's connection theory on fibre bundles. Pioneer work was done between 1880 and 1940 by H. Poincare, I. Bendixson, H. Kneser, H. Whitney, and IV. Kaplan - to name a few - who all studied "regular curve families" on surfaces, and later by Ch. Ehresmann, G. Reeb, A. Haefliger and otners between 1940 and 1960. Since then the subject has developed from a collection of a few papers to a wide field of research. ~owadays, one usually distinguishes between two main branches of foliation theory, the so-called quantitative theory (including homotopy theory and cnaracteristic classes) on the one hand, and the qualitative or geometrie theory on the other. The present volume is the first part of a monograph on geometrie aspects of foliations. Our intention here is to present some fundamental concepts and results as weIl as a great number of ideas and examples of various types. The selection of material from only one branch of the theory is conditioned not only by the authors' personal interest but also by the wish to give a systematic and detailed treatment, including complete proofs of all main results. We hope that tilis goal has been achieved
Introduction to the Geometry of Foliations, Part B
Language: de
Pages: 298
Authors: Gilbert Hector
Categories: Mathematics
Type: BOOK - Published: 2013-03-09 - Publisher: Springer-Verlag

Books about Introduction to the Geometry of Foliations, Part B
Introduction to the Geometry of Foliations, Part A
Language: en
Pages: 236
Authors: Gilbert Hector
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

Foliation theory grew out of the theory of dynamical systems on manifolds and Ch. Ehresmann's connection theory on fibre bundles. Pioneer work was done between 1880 and 1940 by H. Poincare, I. Bendixson, H. Kneser, H. Whitney, and IV. Kaplan - to name a few - who all studied "regular
Introduction to the Geometry of Foliations, Part B
Language: en
Pages: 298
Authors: Gilbert Hector, Ulrich Hirsch
Categories: Technology & Engineering
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

"The book ...is a storehouse of useful information for the mathematicians interested in foliation theory." (John Cantwell, Mathematical Reviews 1992)
Introduction to the Geometry of Foliations, Part A
Language: de
Pages: 236
Authors: Gilbert Hector, Ulrich Hirsch
Categories: Science
Type: BOOK - Published: 2012-11-09 - Publisher: Vieweg+Teubner Verlag

Foliation theory grew out of the theory of dynamical systems on manifolds and Ch. Ehresmann's connection theory on fibre bundles. Pion~er work was done between 1880 and 1940 by H. Poincare, I. Bendixson, H. Kneser, H. Whitney, and W. Kaplan - to name a few - who all studied "regular
Geometry of Foliations
Language: en
Pages: 310
Authors: Philippe Tondeur
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

The topics in this survey volume concern research done on the differential geom etry of foliations over the last few years. After a discussion of the basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning