Geometry I: Basic Ideas and Concepts of Differential Geometry: 28 (Encyclopaedia of Mathematical Sciences, 28)

R.V. Gamkrelidze, D.V. Alekseevskij, V.V. Lychagin, A.M. Vinogradov, E. Primrose

ISBN 10: 3540519998 / ISBN 13: 9783540519997

Editore: Springer 1991-11-07, 1991

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Codice articolo 6666-GRD-9783540519997

Dati bibliografici

• Titolo: Geometry I: Basic Ideas and Concepts of Differential Geometry: 28 (Encyclopaedia of Mathematical Sciences, 28)
• Editore: Springer 1991-11-07
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 3540519998
• ISBN 13: 9783540519997
• Rilegatura: Hardcover
• Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

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.