Geometry I

Basic Ideas and Concepts of Differential Geometry
1. Auflage. Softcover version of original hardcover Auflage 1991
ISBN: 978-3-642-08085-2
Verlag: Springer

Buch, Englisch, 266 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 423 g

Reihe: Encyclopaedia of Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Gamkrelidze, R. V.

Weitere Mitwirkende

Primrose, E.

Alekseevskij, D.V.

Lychagin, V.V.

Vinogradov, A.M.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Euklidische Geometrie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

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.