Extrinsic geometry of foliations / Vladimir Rovenski, Paweł Walczak.

By:

Rovenskii, Vladimir Y, 1953- [author.]

Contributor(s):

Walczak, Paweł Grzegorz [author.]

Material type: Text

text
still image

Media type:

unmediated

Carrier type:

volume

ISBN:

9783030700669
3030700666

Subject(s):

DDC classification:

514.72 R873e

Summary: 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.

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Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	Castorina Estantes Abertas (Open Shelves)	Livros (Books)	514.72 R873e 2021 IMPA (Browse shelf(Opens below))	1	Available		39063000808202

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Previous	514.72 R197a 2003 IMPA Algebraic and geometric surgery/	514.72 R248l 1984 IMPA Liftings, homotopy liftings and localization applied to vector field and immersion theory/	514.72 R371d 1983 IMPA Differential geometry of foliations: the fundamental integrability problem/	514.72 R873e 2021 IMPA Extrinsic geometry of foliations /	514.72 S471 1972 IMPA Seminar on differential topology. Brandeis, 1972: Proceedings.	514.72 S471 1972 IMPA Seminar on differential topology. Brandeis, 1972: Proceedings.	514.72 S632e 1970 IMPA Exterior forms and their applications/	Next

Includes bibliographical references (pages 303-312) and index.

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.

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