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Cover: 9783030700690 | Extrinsic Geometry of Foliations | Pawe¿ Walczak (u. a.) | Taschenbuch
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Extrinsic Geometry of Foliations
Taschenbuch von Pawe¿ Walczak (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
Vladimir Rovenski (University of Haifa) and Pawe¿ Walczak (University of Lodz), are well-known scientists, specializing in differential geometry, topology and dynamics of foliations. Their scientific contact began in May/June of 1995 during the International Conference "Foliations: Geometry and Dynamics" in Warsaw. Their common interests in Riemannian geometry of foliations and submanifolds sparked the beginning of their scientific co-operation. The authors formed a common theme of research and the idea of a scientific relay race. The scientific relay race was started by Prof. Walczak who had won a Marie Curie grant and conducted research at Institut de Mathématiques de Bourgogne (Dijon, France) from 2003-2005. Prof. Rovenski won a similar Marie Curie grant and conducted research in cooperation with Walczak at the University of Lodz from 2008-2010. Their scientific synergies ongoing, and the scientific relay race is successfully continued by their students. The collaboration and friendship of the authors for over 25 years has led to several scientific works in extrinsic geometry of foliations of Riemannian and Finsler manifolds.
Zusammenfassung

Problems of prescribing the extrinsic geometry and curvature of foliations are central to the book

Presents the state of the art in geometric and analytical theory of foliations

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

Inhaltsverzeichnis
Preface.- 1. Preliminaries.- 2. Integral formulas.- 3. Prescribing the mean curvature.- 4. Variational formulae.- 5. Extrinsic Geometric flows.- References.- Index.
Details
Erscheinungsjahr: 2022
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Progress in Mathematics
Inhalt: xiii
319 S.
16 s/w Illustr.
6 farbige Illustr.
319 p. 22 illus.
6 illus. in color.
ISBN-13: 9783030700690
ISBN-10: 3030700690
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Walczak, Pawe¿
Rovenski, Vladimir
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Progress in Mathematics
Maße: 235 x 155 x 19 mm
Von/Mit: Pawe¿ Walczak (u. a.)
Erscheinungsdatum: 24.05.2022
Gewicht: 0,511 kg
Artikel-ID: 121563896
Über den Autor
Vladimir Rovenski (University of Haifa) and Pawe¿ Walczak (University of Lodz), are well-known scientists, specializing in differential geometry, topology and dynamics of foliations. Their scientific contact began in May/June of 1995 during the International Conference "Foliations: Geometry and Dynamics" in Warsaw. Their common interests in Riemannian geometry of foliations and submanifolds sparked the beginning of their scientific co-operation. The authors formed a common theme of research and the idea of a scientific relay race. The scientific relay race was started by Prof. Walczak who had won a Marie Curie grant and conducted research at Institut de Mathématiques de Bourgogne (Dijon, France) from 2003-2005. Prof. Rovenski won a similar Marie Curie grant and conducted research in cooperation with Walczak at the University of Lodz from 2008-2010. Their scientific synergies ongoing, and the scientific relay race is successfully continued by their students. The collaboration and friendship of the authors for over 25 years has led to several scientific works in extrinsic geometry of foliations of Riemannian and Finsler manifolds.
Zusammenfassung

Problems of prescribing the extrinsic geometry and curvature of foliations are central to the book

Presents the state of the art in geometric and analytical theory of foliations

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

Inhaltsverzeichnis
Preface.- 1. Preliminaries.- 2. Integral formulas.- 3. Prescribing the mean curvature.- 4. Variational formulae.- 5. Extrinsic Geometric flows.- References.- Index.
Details
Erscheinungsjahr: 2022
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Progress in Mathematics
Inhalt: xiii
319 S.
16 s/w Illustr.
6 farbige Illustr.
319 p. 22 illus.
6 illus. in color.
ISBN-13: 9783030700690
ISBN-10: 3030700690
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Walczak, Pawe¿
Rovenski, Vladimir
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Progress in Mathematics
Maße: 235 x 155 x 19 mm
Von/Mit: Pawe¿ Walczak (u. a.)
Erscheinungsdatum: 24.05.2022
Gewicht: 0,511 kg
Artikel-ID: 121563896
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