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Differential Geometry of Curves and Surfaces

A Concise Guide

Authors: Toponogov, Victor Andreevich

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eBook 51,16 €
price for Spain (gross)
  • ISBN 978-0-8176-4402-4
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-0-8176-4384-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.

Reviews

From the reviews:

"This book by the late author covers … the subjects which are normally taught in a course on the differential geometry of curves and surfaces. … It can be recommended for first-year graduate students and also for use in the classroom. … the book is rich in geometry and concrete examples. … the book is very welcome since it is an original contribution in various aspects and gives a number of geometric insights … . Numerous illustrations make the reading enjoyable." (Wolfgang Kühnel, Mathematical Reviews, Issue 2006 m)

"Toponogov’s ‘concise guide’ to elementary differential geometry has the potential to be a useful reference and/or review book … ."(Fernando Q. Gouvèa, MathDL, March, 2006)

“This book, written by one of the Russian masters, offers a comprehensive introduction to classical differential geometry of curves and surfaces. Only a basic background in analysis and linear algebra is needed to follow the presentation. … A distinctive feature of the book is that, apart from a large number of exercises, it also contains many original problems with outlines of solutions.” (A. Cap, Monatshefte für Mathematik, Vol. 155 (1), September, 2008)


Table of contents (3 chapters)

Table of contents (3 chapters)
  • Theory of Curves in Three-dimensional Euclidean Space and in the Plane

    Pages 1-63

  • Extrinsic Geometry of Surfaces in Three-dimensional Euclidean Space

    Pages 65-150

  • Intrinsic Geometry of Surfaces

    Pages 151-197

Buy this book

eBook 51,16 €
price for Spain (gross)
  • ISBN 978-0-8176-4402-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-0-8176-4384-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Differential Geometry of Curves and Surfaces
Book Subtitle
A Concise Guide
Authors
Copyright
2006
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4402-4
DOI
10.1007/b137116
Softcover ISBN
978-0-8176-4384-3
Edition Number
1
Number of Pages
XIV, 206
Number of Illustrations
70 b/w illustrations
Topics