Basic ideas and concepts of differential geometry
著者
書誌事項
Basic ideas and concepts of differential geometry
（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 28 . Geometry / R.V. Gamkrelidze (ed.) ; 1）
Springer-Verlag, c1991
- : gw
- : us
- タイトル別名
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Geometrii︠a︡ I
Geometry I
Geometry one
Geometry 1
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注記
Translation of: Geometrii︠a︡ I, issued as v. 28 of the serial: Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalʹnye napravlenii︠a︡
Bibliography: p. 249-255
Include indexes
内容説明・目次
内容説明
This book provides a tour of the principal areas and methods of modern differential geometry. Beginning at the introductory level with curves in Euclidian space, the sections become more challenging, arriving finally at the advanced topics that form the greatest part of the book: transformation groups, the geometry of differential equations, geometric structures, the equivalence problem, the geometry of elliptic operators.
目次
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.
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