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Differential Geometry of Curves and Surfaces
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Differential Geometry of Curves and Surfaces

Differential Geometry of Curves and Surfaces

A Concise Guide

Victor A. Toponogov

206 pages, parution le 31/10/2005

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

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