Differential Geometry of Curves and Surfaces

A Concise Guide

Victor A. Toponogov

206 pages, parution le 31/10/2005

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Résumé

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:

Covers central concepts including curves, surfaces, geodesics, and intrinsic geometry
Substantive material on the Aleksandrov global angle comparison theorem, which the author generalized for Riemannian manifolds (a result now known as the celebrated Toponogov Comparison Theorem, one of the cornerstones of modern Riemannian geometry)
Contains many nontrivial and original problems, some with hints and solutions

This rigorous exposition, with well-motivated topics, is ideal for advanced undergraduate and first-year graduate students seeking to enter the fascinating world of geometry.

Sommaire

Preface
About the Author
Theory in Three-Dimensional Euclidean Space and in the Plane
Extrinsic Geometry of Surfaces in Three-Dimensional Euclidean Space
Intrinsic of Surfaces
References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Victor A. Toponogov
Parution	31/10/2005
Nb. de pages	206
Format	15,5 x 23,5
Couverture	Broché
Poids	385g
Intérieur	Noir et Blanc
EAN13	9780817643843
ISBN13	978-0-8176-4384-3