Elementary Topics in Differential Geometry

Name: Elementary Topics in Differential Geometry
Price: 9.19 USD
Availability: InStock
ISBN: 9780387903576

ISBN-10: 0387903577

ISBN-13: 9780387903576

Edition: 1979

Authors: J. A. Thorpe

List price: $79.95

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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,…

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