Elementary Topics in Differential Geometry

ISBN-10: 0387903577

ISBN-13: 9780387903576

Edition: 1979

Authors: J. A. Thorpe

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Description:

This introductory text develops the geometry of n-dimensional oriented surfaces in Rn+1. By viewing such surfaces as level sets of smooth functions, the author is able to introduce global ideas early without the need for preliminary chapters developing sophisticated machinery. the calculus of vector fields is used as the primary tool in developing the theory. Coordinate patches are introduced only after preliminary discussions of geodesics, parallel transport, curvature, and convexity. Differential forms are introduced only as needed for use in integration. The text, which draws significantly on students' prior knowledge of linear algebra, multivariate calculus, and differential equations, is designed for a one-semester course at the junior/senior level.
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Book details

List price: $79.95
Copyright year: 1979
Publisher: Springer
Publication date: 10/27/1994
Binding: Hardcover
Pages: 256
Size: 6.50" wide x 9.75" long x 0.75" tall
Weight: 1.232
Language: English

Contents: Graphs and Level Sets
Vector Fields
The Tangent Space
Surfaces
Vector Fields on Surfaces
Orientation
The Gauss Map
Geodesics
Parallel Transport
The Weingarten Map
Curvature of Plane Curves
Arc Length and Line Integrals
Curvature of Surfaces
Convex Surfaces
Parametrized Surfaces
Local Equivalence of Surfaces and Parametrized Surfaces
Focal Points
Surface Area and Volume
Minimal Surfaces
The Exponential Map
Surfaces with Boundary
The Gauss-Bonnet Theorem
Rigid Motions and Congruence
Isometries
Riemannian Metrics
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