Topics In Extrinsic Geometry Of Codimension One Foliations

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Topics In Extrinsic Geometry Of Codimension One Foliations

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Author :
language : en
Publisher:
Release Date : 2011-08-07

Topics In Extrinsic Geometry Of Codimension One Foliations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-07 with categories.

Topics In Extrinsic Geometry Of Codimension One Foliations

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Author : Vladimir Rovenski
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-26

Topics In Extrinsic Geometry Of Codimension One Foliations written by Vladimir Rovenski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-26 with Mathematics categories.

Extrinsic 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 formulae involve the Newton transformations of the Weingarten operator. The central topic of this book is Extrinsic Geometric Flow (EGF) on foliated manifolds, which may be a tool for prescribing extrinsic geometric properties of foliations. To develop EGF, one needs Variational Formulae, revealed in chapter 2, which expresses a change in different extrinsic geometric quantities of a fixed foliation under leaf-wise variation of the Riemannian Structure of the ambient manifold. Chapter 3 defines a general notion of EGF and studies the evolution of Riemannian metrics along the trajectories of this flow(e.g., describes the short-time existence and uniqueness theory and estimate the maximal existence time).Some special solutions (called Extrinsic Geometric Solutions) of EGF are presented and are of great interest, since they provide Riemannian Structures with very particular geometry of the leaves. This work is aimed at those who have an interest in the differential geometry of submanifolds and foliations of Riemannian manifolds.

Extrinsic Geometry Of Foliations

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Author : Vladimir Rovenski
language : en
Publisher: Springer Nature
Release Date : 2021-05-22

Extrinsic Geometry Of Foliations written by Vladimir Rovenski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-22 with Mathematics categories.

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.

Introduction To The Geometry Of Foliations Part B

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Author : Gilbert Hector
language : de
Publisher: Springer-Verlag
Release Date : 2013-03-09

Introduction To The Geometry Of Foliations Part B written by Gilbert Hector and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Geometry And Its Applications

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Author : Vladimir Rovenski
language : en
Publisher: Springer
Release Date : 2014-05-05

Geometry And Its Applications written by Vladimir Rovenski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-05 with Mathematics categories.

This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work is based on the second international workshop entitled "Geometry and Symbolic Computations," held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and its applications in fields such as computer science, tomography and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometric modeling using symbolic programs such as MapleTM and Mathematica® , as well as presentation of new results.

Foliations 2012 Proceedings Of The International Conference

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Author : Jesus A Alvarez Lopez
language : en
Publisher: World Scientific
Release Date : 2013-10-25

Foliations 2012 Proceedings Of The International Conference written by Jesus A Alvarez Lopez and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-25 with Mathematics categories.

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.

Introduction To The Geometry Of Foliations Part B

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Author : Gilbert Hector
language : en
Publisher: Vieweg+Teubner Verlag
Release Date : 1981

Introduction To The Geometry Of Foliations Part B written by Gilbert Hector and has been published by Vieweg+Teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.

Introduction To The Geometry Of Foliations

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Author :
language : en
Publisher:
Release Date : 1987

Introduction To The Geometry Of Foliations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.

Geometry Of Foliations

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Author : Philippe Tondeur
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Geometry Of Foliations written by Philippe Tondeur and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2007

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.