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Introduction to Foliations and Lie Groupoidsby I. Moerdijk; J. Mrcun; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak
Cambridge University Press 2003; US$ 60.00This book gives a quick introduction to the theory of foliations and Lie groupoids. It is based on the authors' extensive teaching experience and contains numerous examples and exercises making it ideal either for independent study or as the basis of a graduate course. more...
Foliations and Geometric Structuresby Aurel Bejancu; Hani Reda Farran
Springer 2006; US$ 129.00Offers 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. more...
Foliations and the Geometry of 3-Manifoldsby Danny Calegari
Oxford University Press, UK 2007; US$ 150.00This 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. - ;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... more...
Metric Foliations and Curvatureby Detlef Gromoll; Gerard Walschap
Springer 2008; US$ 69.95Riemannian 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. more...
Topics in Extrinsic Geometry of Codimension-One Foliationsby Vladimir Rovenski; Pawel Walczak
Springer 2011; US$ 49.95Extrinsic geometry describes properties of foliations on Riemannian manifolds which can be expressed in terms of the second fundamental form of the leaves. The authors of Topics in Extrinsic Geometry of Codimension-One Foliations achieve a technical tour de force, which will lead to important geometric results. The Integral Formulae, introduced in chapter 1, is a useful for problems such as: prescribing higher mean curvatures of foliations, minimizing volume and energy defined for vector or plane fields on manifolds, and existence of foliations whose leaves enjoy given geometric properties. The Integral Formulae steams from a Reeb formula, for foliations on space forms which generalize the classical ones. For a special auxiliary functions the... more...
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