Introduction to the Geometry of Foliations, Part A PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Introduction to the Geometry of Foliations, Part A PDF full book. Access full book title Introduction to the Geometry of Foliations, Part A by Gilbert Hector. Download full books in PDF and EPUB format.
Author: Gilbert Hector Publisher: Springer Science & Business Media ISBN: 3322901157 Category : Mathematics Languages : en Pages : 247
Book Description
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
Author: Gilbert Hector Publisher: Springer Science & Business Media ISBN: 3322901610 Category : Technology & Engineering Languages : en Pages : 309
Book Description
"The book ...is a storehouse of useful information for the mathematicians interested in foliation theory." (John Cantwell, Mathematical Reviews 1992)
Author: Philippe Tondeur Publisher: Springer Science & Business Media ISBN: 9783764357412 Category : Gardening Languages : en Pages : 330
Book Description
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
Author: Gilbert Hector Publisher: Vieweg+Teubner Verlag ISBN: 9783528185688 Category : Technology & Engineering Languages : en Pages : 0
Book Description
"The book ...is a storehouse of useful information for the mathematicians interested in foliation theory." (John Cantwell, Mathematical Reviews 1992)
Author: Philippe Tondeur Publisher: Birkhäuser ISBN: 3034889143 Category : Mathematics Languages : en Pages : 308
Book Description
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 with Chapter 5. Following the discussion of the special case of flows in Chapter 6, Chapters 7 and 8 are de voted to Hodge theory for the transversal Laplacian and applications of the heat equation method to Riemannian foliations. Chapter 9 on Lie foliations is a prepa ration for the statement of Molino's Structure Theorem for Riemannian foliations in Chapter 10. Some aspects of the spectral theory for Riemannian foliations are discussed in Chapter 11. Connes' point of view of foliations as examples of non commutative spaces is briefly described in Chapter 12. Chapter 13 applies ideas of Riemannian foliation theory to an infinite-dimensional context. Aside from the list of references on Riemannian foliations (items on this list are referred to in the text by [ ]), we have included several appendices as follows. Appendix A is a list of books and surveys on particular aspects of foliations. Appendix B is a list of proceedings of conferences and symposia devoted partially or entirely to foliations. Appendix C is a bibliography on foliations, which attempts to be a reasonably complete list of papers and preprints on the subject of foliations up to 1995, and contains approximately 2500 titles.
Author: Vladimir Rovenski Publisher: Springer Nature ISBN: 3030700674 Category : Mathematics Languages : en Pages : 319
Book Description
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.