Modern Geometry — Methods and Applications: Part I. The Geometry of Surfaces, Transformation Groups, and Fields

B. A. Dubrovin, A. T. Fomenko, S. P. Novikov (auth.)0387976639, 9780387976631, 3540976639

This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised.

---

Table of contents :
Front Matter….Pages i-xv
Geometry in Regions of a Space. Basic Concepts….Pages 1-60
The Theory of Surfaces….Pages 61-144
Tensors: The Algebraic Theory….Pages 145-233
The Differential Calculus of Tensors….Pages 234-312
The Elements of the Calculus of Variations….Pages 313-374
The Calculus of Variations in Several Dimensions. Fields and Their Geometric Invariants….Pages 375-454
Back Matter….Pages 455-464