
Geometry I
Basic Ideas and Concepts of Differential Geometry
R.V. Gamkrelidze(Editor)
Springer (Publisher)
Published on 7. November 1991
Book
Hardback
V, 266 pages
978-3-540-51999-7 (ISBN)
Description
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.
More details
Series
Edition
1991 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
V, 266 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 21 mm
Weight
582 gr
ISBN-13
978-3-540-51999-7 (9783540519997)
DOI
10.1007/978-3-662-02712-7
Schweitzer Classification
Other editions
Additional editions

Book
12/2010
Springer
€139.09
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Persons
Editor
Contributions
Translation
Content
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.