Foliations And Geometric Structures
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Foliations And Geometric Structures
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Author : Aurel Bejancu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-17
Foliations And Geometric Structures written by Aurel Bejancu 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 2006-01-17 with Mathematics categories.
Offers basic material on distributions and foliations. This book introduces and builds the tools needed for studying the geometry of foliated manifolds. Its main theme is to investigate the interrelations between foliations of a manifold on the one hand, and the many geometric structures that the manifold may admit on the other hand.
Foliations And Geometric Structures
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Author : Aurel Bejancu
language : en
Publisher: Springer
Release Date : 2009-09-03
Foliations And Geometric Structures written by Aurel Bejancu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-03 with Mathematics categories.
Foliations And The Geometry Of 3 Manifolds
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Author : Danny Calegari
language : en
Publisher: Clarendon Press
Release Date : 2007-05-17
Foliations And The Geometry Of 3 Manifolds written by Danny Calegari and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-17 with Mathematics categories.
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in 1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Geometry Of Foliations
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Author : Philippe Tondeur
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-05
Geometry Of Foliations written by Philippe Tondeur 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 1997-05 with Gardening categories.
Surveys research over the past few years at a level accessible to graduate students and researchers with a background in differential and Riemannian geometry. Among the topics are foliations of codimension one, holonomy, Lie foliations, basic forms, mean curvature, the Hodge theory for the transversal Laplacian, applications of the heat equation method to Riemannian foliations, the spectral theory, Connes' perspective of foliations as examples of non- commutative spaces, and infinite-dimensional examples. The bibliographic appendices list books and surveys on particular aspects of foliations, proceedings of conferences and symposia, all papers on the subject up to 1995, and the numbers of papers published on the subject during the years 1990-95. Annotation copyrighted by Book News, Inc., Portland, OR
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"".
Riemannian Foliations
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Author : Molino
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Riemannian Foliations written by Molino 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 has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no singularities, then its trajectories form a par tition of M into curves, i.e. a foliation of codimension n - 1. More generally, a foliation F of codimension q on M corresponds to a partition of M into immersed submanifolds [the leaves] of dimension ,--------,- - . - -- p = n - q. The first global image that comes to mind is 1--------;- - - - - - that of a stack of "plaques". 1---------;- - - - - - Viewed laterally [transver 1--------1- - - -- sally], the leaves of such a 1--------1 - - - - -. stacking are the points of a 1--------1--- ----. quotient manifold W of di L..... -' _ mension q. -----~) W M Actually, this image corresponds to an elementary type of folia tion, that one says is "simple". For an arbitrary foliation, it is only l- u L ally [on a "simpIe" open set U] that the foliation appears as a stack of plaques and admits a local quotient manifold. Globally, a leaf L may - - return and cut a simple open set U in several plaques, sometimes even an infinite number of plaques.
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.
Foliations Ii
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Author : Alberto Candel
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Foliations Ii written by Alberto Candel 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 2000 with Mathematics categories.
This is the second of two volumes on foliations (the first is Volume 23 of this series). In this volume, three specialized topics are treated: analysis on foliated spaces, characteristic classes of foliations, and foliated three-manifolds. Each of these topics represents deep interaction between foliation theory and another highly developed area of mathematics. In each case, the goal is to provide students and other interested people with a substantial introduction to the topic leading to further study using the extensive available literature.
Geometry Dynamics And Topology Of Foliations
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Author : Bruno Scárdua
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017
Geometry Dynamics And Topology Of Foliations written by Bruno Scárdua and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
The geometric theory of foliations is one of the fields in mathematics that gathers several distinct domains: topology, dynamical systems, differential topology and geometry, among others. Containing material dating from the origins of the theory of foliations, this volume also brings readers to the heart of recent results in the field.
Extrinsic Geometry Of Foliations
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Author : Vladimir Rovenski
language : en
Publisher: Springer Nature
Release Date : 2021-05-22
Extrinsic Geometry Of Foliations written by Vladimir Rovenski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-22 with Mathematics categories.
This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics. The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.