Differential Geometry of Curves and Surfaces

A Concise Guide

  • Victor A. Toponogov
  • Vladimir Y. Rovenski

Table of contents

About this book


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.


Riemannian geometry curvature differential geometry ksa manifold

Authors and affiliations

  • Victor A. Toponogov
    • 1
  1. 1.Department of Analysis and Geometry, Sobolev Institute of MathematicsSiberian Branch of the Russian Academy of SciencesRussia

Editors and affiliations

  • Vladimir Y. Rovenski
    • 1
  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael

Bibliographic information