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Geometry of Foliations
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Catalogue Information
Field name
Details
Dewey Class
516.36
Title
Geometry
of
Foliations ([EBook] /) / by Philippe Tondeur.
Author
Tondeur, Philippe
Other name(s)
SpringerLink (Online service)
Publication
Basel : : Birkhäuser Basel : : Imprint: Birkhäuser, , 1997.
Physical Details
VIII, 310 p. : online resource.
Series
Monographs in mathematics
; 90
ISBN
9783034889148
Summary Note
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.:
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-0348-8914-8
Links to Related Works
Subject References:
Differential Geometry
.
Geometry
.
Mathematics
.
Authors:
Tondeur, Philippe
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Monographs in mathematics
.
Classification:
516.36
.
.
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