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Cover: 9783540519997 | Geometry I | Basic Ideas and Concepts of Differential Geometry | Buch
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Geometry I
Basic Ideas and Concepts of Differential Geometry
Buch von R. V. Gamkrelidze
Sprache: Englisch

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Beschreibung
Since the early work of Gauss and Riemann, differential geometry has grown into a vast network of ideas and approaches, encompassing local considerations such as differential invariants and jets as well as global ideas, such as Morse theory and characteristic classes. In this volume of the Encyclopaedia, the authors give a tour of the principal areas and methods of modern differential geomerty. The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry. Beginning at the introductory level with curves in Euclidian space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book: transformation groups, the geometry of differential equations, geometric structures, the equivalence problem, the geometry of elliptic operators. Several of the topics are approaches which are now enjoying a resurgence, e.g. G-structures and contact geometry. As an overview of the major current methods of differential geometry, EMS 28 is a map of these different ideas which explains the interesting points at every stop. The authors' intention is that the reader should gain a new understanding of geometry from the process of reading this survey.
Since the early work of Gauss and Riemann, differential geometry has grown into a vast network of ideas and approaches, encompassing local considerations such as differential invariants and jets as well as global ideas, such as Morse theory and characteristic classes. In this volume of the Encyclopaedia, the authors give a tour of the principal areas and methods of modern differential geomerty. The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry. Beginning at the introductory level with curves in Euclidian space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book: transformation groups, the geometry of differential equations, geometric structures, the equivalence problem, the geometry of elliptic operators. Several of the topics are approaches which are now enjoying a resurgence, e.g. G-structures and contact geometry. As an overview of the major current methods of differential geometry, EMS 28 is a map of these different ideas which explains the interesting points at every stop. The authors' intention is that the reader should gain a new understanding of geometry from the process of reading this survey.
Zusammenfassung
In this volume of the Encyclopaedia, the authors give a tour of the principal areas and methods of modern differential geometry. Some topics, though important, have not previously appeared in books with a general readership. The book is structured to allow the reader to skip about the text, rather than systematically reading from beginning to end. Compared to other EMS volumes, EMS 28 has an increased appeal for early graduate students.
Inhaltsverzeichnis
1. Introduction: A Metamathematical View of Differential Geometry.- 2. The Geometry of Surfaces.- 3. The Field Approach of Riemann.- 4. The Group Approach of Lie and Klein. The Geometry of Transformation Groups.- 5. The Geometry of Differential Equations.- 6. Geometric Structures.- 7. The Equivalence Problem, Differential Invariants and Pseudogroups.- 8. Global Aspects of Differential Geometry.- Commentary on the References.- References.- Author Index.
Details
Erscheinungsjahr: 1991
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Encyclopaedia of Mathematical Sciences
Inhalt: v
266 S.
62 s/w Illustr.
ISBN-13: 9783540519997
ISBN-10: 3540519998
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Redaktion: Gamkrelidze, R. V.
Herausgeber: R V Gamkrelidze
Übersetzung: Primrose, E.
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Encyclopaedia of Mathematical Sciences
Maße: 241 x 160 x 21 mm
Von/Mit: R. V. Gamkrelidze
Erscheinungsdatum: 07.11.1991
Gewicht: 0,582 kg
Artikel-ID: 102459340
Zusammenfassung
In this volume of the Encyclopaedia, the authors give a tour of the principal areas and methods of modern differential geometry. Some topics, though important, have not previously appeared in books with a general readership. The book is structured to allow the reader to skip about the text, rather than systematically reading from beginning to end. Compared to other EMS volumes, EMS 28 has an increased appeal for early graduate students.
Inhaltsverzeichnis
1. Introduction: A Metamathematical View of Differential Geometry.- 2. The Geometry of Surfaces.- 3. The Field Approach of Riemann.- 4. The Group Approach of Lie and Klein. The Geometry of Transformation Groups.- 5. The Geometry of Differential Equations.- 6. Geometric Structures.- 7. The Equivalence Problem, Differential Invariants and Pseudogroups.- 8. Global Aspects of Differential Geometry.- Commentary on the References.- References.- Author Index.
Details
Erscheinungsjahr: 1991
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Encyclopaedia of Mathematical Sciences
Inhalt: v
266 S.
62 s/w Illustr.
ISBN-13: 9783540519997
ISBN-10: 3540519998
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Redaktion: Gamkrelidze, R. V.
Herausgeber: R V Gamkrelidze
Übersetzung: Primrose, E.
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Encyclopaedia of Mathematical Sciences
Maße: 241 x 160 x 21 mm
Von/Mit: R. V. Gamkrelidze
Erscheinungsdatum: 07.11.1991
Gewicht: 0,582 kg
Artikel-ID: 102459340
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