In diesem Band der Encyclopaedia geben die Autoren einen Überblick über die wichtigsten Gebiete und Methoden der Differentialgeometrie. Einige der Themen, obwohl von großer Wichtigkeit, wurden bisher in Büchern mit einem großen Leserkreis nicht angesprochen. Der Aufbau des Buches gestattet es dem Leser, eine Auswahl zu treffen, anstatt es systematisch von Anfang bis Ende durchzulesen. Stärker als andere EMS-Bände spricht EMS 28 auch Studenten höherer Semester an.

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.

Klappentext

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.

Inhalt

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.