Overview

This text describes work on the differential geometry of foliations, in particular Riemannian foliations, done in the last few years. Sections on the Hodge theory for the transversal Laplace operator, and on applications of the heat equation method to Riemannian foliations are of particular note. There are chapters on the spectral theory for Riemannian foliations, on the author's point of view of foliations as examples of noncommutative spaces, and on infinite-dimensional examples of Riemannian foliations.

Full Product Details

Author:   Philippe Tondeur
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   1997 ed.
Volume:   90
Dimensions:   Width: 15.50cm , Height: 1.90cm , Length: 23.50cm
Weight:   0.653kg
ISBN:  

9783764357412

ISBN 10:   376435741
Pages:   310
Publication Date:   01 May 1997
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Examples and Definition of Foliations.- 2 Foliations of Codimension One.- 3 Holonomy, Second Fundamental Form, Mean Curvature.- 4 Basic Forms, Spectral Sequence, Characteristic Form.- 5 Transversal Riemannian Geometry.- 6 Flows.- 7 Hodge Theory for the Transversal Laplacian.- 8 Cohomology Vanishing and Tautness.- 9 Lie Foliations.- 10 Structure of Riemannian Foliations.- 11 Spectral Geometry of Riemannian Foliations.- 12 Foliations as Noncommutative Spaces.- 13 Infinite-Dimensional Riemannian Foliations.- References on Riemannian Foliations.- Appendix A Books and Surveys on Particular Aspects of Foliations.- Appendix B Proceedings of Conferences and Symposia devoted to Foliations.- Appendix C Bibliography on Foliations. This should be a reasonably complete list of all papers on the subject of foliations up to 1995.- Appendix D Numbers of papers on foliations published during consecutive five year periods up to 1995.- Index of Subjects.- Index of Notations.

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