Differential Geometry of Curves and Surfaces A Concise Guide

Name: Differential Geometry of Curves and Surfaces A Concise Guide
Price: 17.24 USD
Availability: InStock
ISBN: 9780817643843

ISBN-10: 0817643842

ISBN-13: 9780817643843

Edition: 2006

Authors: Victor A. Toponogov, Vladimir Rovenski, Sobolev Institute of Mathematics sTAFF

List price: $69.95

30 day, 100% satisfaction guarantee!

Marketplace

2 new & used from $17.24

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

Description:

The study of curves and surfaces forms an important part of classical differential geometry. Differential Geometry of Curves and Surfaces: A Concise Guide presents traditional material in this field along with important ideas of Riemannian geometry. The reader is introduced to curves, then to surfaces, and finally to more complex topics. Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels.Key topics and features:* Coversnbsp;central concepts including curves, surfaces, geodesics, and intrinsic geometry* Substantive material on the Aleksandrov global angle comparison theorem, which the…

Book details

List price: $69.95
Copyright year: 2006
Publisher: Birkhauser Boston
Publication date: 12/5/2005
Binding: Paperback
Pages: 206
Size: 6.25" wide x 9.50" long x 0.75" tall
Weight: 0.836
Language: English



Preface


About the Author



Theory of Curves in Three-dimensional Euclidean Space and in the Plane



Preliminaries



Definition and Methods of Presentation of Curves



Tangent Line and Osculating Plane



Length of a Curve



Problems: Convex Plane Curves



Curvature of a Curve



Problems: Curvature of Plane Curves



Torsion of a Curve



The Frenet Formulas and the Natural Equation of a Curve



Problems: Space Curves



Phase Length of a Curve and the Fenchel-Reshetnyak Inequality



Exercises to Chapter 1



Extrinsic Geometry of Surfaces in Three-dimensional Euclidean Space



Definition and Methods of Generating Surfaces



The Tangent Plane



First Fundamental Form of a Surface



Second Fundamental Form of a Surface



The Third Fundamental Form of a Surface



Classes of Surfaces



Some Classes of Curves on a Surface



The Main Equations of Surface Theory



Appendix: Indicatrix of a Surface of Revolution



Exercises to Chapter 2



Intrinsic Geometry of Surfaces



Introducing Notation



Covariant Derivative of a Vector Field



Parallel Translation of a Vector along a Curve on a Surface



Geodesics



Shortest Paths and Geodesics



Special Coordinate Systems



Gauss-Bonnet Theorem and Comparison Theorem for the Angles of a Triangle



Local Comparison Theorems for Triangles



Aleksandrov Comparison Theorem for the Angles of a Triangle



Problems to Chapter 3


References


Index