This volume takes a look at the current state of the theory of foliations, with surveys and research articles concerning different aspects. The focused aspects cover geometry of foliated Riemannian manifolds, Riemannian foliations and dynamical properties of foliations and some aspects of classical dynamics related to the field. Among the articles readers may find a study of foliations which admit a transverse contractive flow, an extensive survey on non-commutative geometry of Riemannian foliations, an article on contact structures converging to foliations, as well as a few articles on conformal geometry of foliations. This volume also contains a list of open problems in foliation theory which were collected from the participants of the Foliations 2005 conference.

This volume takes a look at the current state of the theory of foliations, with surveys and research articles concerning different aspects. The focused aspects cover geometry of foliated Riemannian manifolds, Riemannian foliations and dynamical properties of foliations and some aspects of classical dynamics related to the field. Among the articles readers may find a study of foliations which admit a transverse contractive flow, an extensive survey on non-commutative geometry of Riemannian foliations, an article on contact structures converging to foliations, as well as a few articles on conformal geometry of foliations. This volume also contains a list of open problems in foliation theory which were collected from the participants of the Foliations 2005 conference.

This volume is a compilation of new results and surveys on the current state of some aspects of the foliation theory presented during the conference “FOLIATIONS 2012”. It contains recent materials on foliation theory which is related to differential geometry, the theory of dynamical systems and differential topology. Both the original research and survey articles found in here should inspire students and researchers interested in foliation theory and the related fields to plan his/her further research.

Presents the proceedings of the conference on Foliations, Geometry, and Topology, held August 6-10, 2007, in Rio de Janeiro, Brazil, in honor of the 70th birthday of Paul Schweitzer. The papers focus on the theory of foliations and related areas such as dynamical systems, group actions on low dimensional manifolds, and geometry of hypersurfaces.

This volume collects a set of contributions by participants of the Workshop Partially hyperbolic dynamics, laminations, and Teichmuller flow held at the Fields Institute in Toronto in January 2006. The Workshop brought together several leading experts in two very active fields of contemporary dynamical systems theory: partially hyperbolic dynamics and Teichmuller dynamics. They are unified by ideas coming from the theory of laminations and foliations, dynamical hyperbolicity, and ergodic theory. These are the main themes of the current volume. The volume contains both surveys and research papers on non-uniform and partial hyperbolicity, on dominated splitting and beyond (in Part I), Teichmuller dynamics with applications to interval exchange transformations and on the topology of moduli spaces of quadratic differentials (in Part II), foliations and laminations and other miscellaneous papers (in Part III). Taken together these papers provide a snapshot of the state of the art in some of the most active topics at the crossroads between dynamical systems, smooth ergodic theory, geometry and topology, suitable for advanced graduate students and researchers.Non-specialists will find the extensive, in-depth surveys especially useful.

This volume takes a look at the current state of the theory of foliations, with surveys and research articles concerning different aspects. The focused aspects cover geometry of foliated Riemannian manifolds, Riemannian foliations and dynamical properties of foliations and some aspects of classical dynamics related to the field. Among the articles readers may find a study of foliations which admit a transverse contractive flow, an extensive survey on non-commutative geometry of Riemannian foliations, an article on contact structures converging to foliations, as well as a few articles on conformal geometry of foliations. This volume also contains a list of open problems in foliation theory which were collected from the participants of the Foliations 2005 conference. Sample Chapter(s). Chapter 1: Morphisms of Pseudogroups and foliated Maps (808 KB). Contents: Morphisms of Pseudogroups and Foliated Maps (J ulvarez Lpez & X Masa); On Infinitesimal Derivatives of the Bott Class (T Asuke); Hirsch Foliations in Codimension Greater Than One (A Bis, S Hurder & J Shive); Extrinsic Geometry of Foliations on 3-Manifolds (D Bolotov); Extrinsic Geometry of Foliations (M Czarnecki & P Walczak); Transversal Twistor Spinors on a Riemannian Foliation (S D Jung); A Survey on Simplicial Volume and Invariants of Foliations and Laminations (T Kuessner); Harmonic Foliations of the Plane, a Conformal Approach (R Langevin); Consecutive Shifts Along Orbits of Vector Fields (S Maksymenko); Generalized Equivariant Index Theory (K Richardson); Vanishing Results for Spectral Terms of a Riemannian Foliation (V Slesar); On the Group of Foliation Preserving Diffeomorphisms (T Tsuboi); and other papers. Readership: Researchers and graduate students in such areas of mathematics as foliations, dynamical systems (Anosov and Morse-Smale, in particular), Riemannian and conformal geometry; and in other fields such as mathematical physics, non-commutative geometry and analysis on manifolds."

This volume contains research and expository papers on recent advances in foliations and Riemannian geometry. Some of the topics covered in this volume include: topology, geometry, dynamics and analysis of foliations, curvature, submanifold theory, Lie groups and harmonic maps.Among the contributions, readers may find an extensive survey on characteristic classes of Riemannian foliations offering also new results, an article showing the uniform simplicity of certain diffeomorphism groups, an exposition of convergences of contact structures to foliations from the point of view of Thurston's and Thurston-Bennequin's inequalities, a discussion about Fatou-Julia decompositions for foliations and a description of singular Riemannian foliations on spaces without conjugate points.Papers on submanifold theory focus on the existence of graphs with prescribed mean curvature and mean curvature flow for spacelike graphs, isometric and conformal deformations and detailed surveys on totally geodesic submanifolds in symmetric spaces, cohomogeneity one actions on hyperbolic spaces and rigidity of geodesic spheres in space forms. Geometric realizability of curvature tensors and curvature operators are also treated in this volume with special attention to the affine and the pseudo-Riemannian settings. Also, some contributions on biharmonic maps and submanifolds enrich the scope of this volume in providing an overview of different topics of current interest in differential geometry.