Geometry I: Basic Ideas and Concepts of Differential Geometry / Edition 1

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

Overview

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.

Product Details

ISBN-13:	9783642080852
Publisher:	Springer Berlin Heidelberg
Publication date:	12/07/2010
Series:	Encyclopaedia of Mathematical Sciences , #28
Edition description:	Softcover reprint of hardcover 1st ed. 1991
Pages:	266
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

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.