Introduction To The Geometry Of Foliations
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Introduction To The Geometry Of Foliations Part A
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Author : Gilbert Hector
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To The Geometry Of Foliations Part A written by Gilbert Hector and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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
Geometric Theory Of Foliations
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Author : César Camacho
language : en
Publisher: Birkhäuser
Release Date : 1984-01-01
Geometric Theory Of Foliations written by César Camacho and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Mathematics categories.
Intuitively, a foliation corresponds to a decomposition of a manifold into a union of connected, disjoint submanifolds of the same dimension, called leaves, which pile up locally like pages of a book. The theory of foliations, as it is known, began with the work of C. Ehresmann and G. Reeb, in the 1940's; however, as Reeb has himself observed, already in the last century P. Painleve saw the necessity of creating a geometric theory (of foliations) in order to better understand the problems in the study of solutions of holomorphic differential equations in the complex field. The development of the theory of foliations was however provoked by the following question about the topology of manifolds proposed by H. Hopf in the 3 1930's: "Does there exist on the Euclidean sphere S a completely integrable vector field, that is, a field X such that X· curl X • 0?" By Frobenius' theorem, this question is equivalent to the following: "Does there exist on the 3 sphere S a two-dimensional foliation?" This question was answered affirmatively by Reeb in his thesis, where he 3 presents an example of a foliation of S with the following characteristics: There exists one compact leaf homeomorphic to the two-dimensional torus, while the other leaves are homeomorphic to two-dimensional planes which accu mulate asymptotically on the compact leaf. Further, the foliation is C"".
Introduction To The Geometry Of Foliations Part B
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Author : Gilbert Hector
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To The Geometry Of Foliations Part B written by Gilbert Hector and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
"The book ...is a storehouse of useful information for the mathematicians interested in foliation theory." (John Cantwell, Mathematical Reviews 1992)
Introduction To Foliations And Lie Groupoids
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Author : I. Moerdijk
language : en
Publisher: Cambridge University Press
Release Date : 2003-09-18
Introduction To Foliations And Lie Groupoids written by I. Moerdijk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-18 with Mathematics categories.
This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.
Introduction To The Geometry Of Foliations
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Author : Gilbert Hector
language : en
Publisher:
Release Date : 2014-01-15
Introduction To The Geometry Of Foliations written by Gilbert Hector and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Topology Of Foliations An Introduction
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Author : Ichirō Tamura
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Topology Of Foliations An Introduction written by Ichirō Tamura and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Foliations (Mathematics). categories.
This book provides historical background and a complete overview of the qualitative theory of foliations and differential dynamical systems. Senior mathematics majors and graduate students with background in multivariate calculus, algebraic and differential topology, differential geometry, and linear algebra will find this book an accessible introduction. Upon finishing the book, readers will be prepared to take up research in this area. Readers will appreciate the book for its highly visual presentation of examples in low dimensions. The author focuses particularly on foliations with compact leaves, covering all the important basic results. Specific topics covered include: dynamical systems on the torus and the three-sphere, local and global stability theorems for foliations, the existence of compact leaves on three-spheres, and foliated cobordisms on three-spheres. Also included is a short introduction to the theory of differentiable manifolds.
Introduction To The Geometry Of Foliations
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Author :
language : en
Publisher:
Release Date : 1987
Introduction To The Geometry Of Foliations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Introduction To The Geometry Of Foliations
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Author : Gilbert HECTOR
language : en
Publisher:
Release Date : 1983
Introduction To The Geometry Of Foliations written by Gilbert HECTOR and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
Metric Foliations And Curvature
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Author : Detlef Gromoll
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-28
Metric Foliations And Curvature written by Detlef Gromoll and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-28 with Mathematics categories.
Riemannian manifolds, particularly those with positive or nonnegative curvature, are constructed from only a handful by means of metric fibrations or deformations thereof. This text documents some of these constructions, many of which have only appeared in journal form. The emphasis is less on the fibration itself and more on how to use it to either construct or understand a metric with curvature of fixed sign on a given space.
Introduction To The Geometry Of Foliations
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Author : Gilbert Hector
language : en
Publisher:
Release Date : 1981
Introduction To The Geometry Of Foliations written by Gilbert Hector and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Science categories.