Differential Geometry of Curves and Surfaces: A Concise Guide

Title	:	Differential Geometry of Curves and Surfaces: A Concise Guide
Authors	:	Victor Andreevich Toponogov
	:	2006 Birkhauser Boston

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
  Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels

This rigorous exposition, with well-motivated topics, is ideal for advanced undergraduate, first-year graduate students seeking to enter the fascinating world of geometry, and students specializing in geometry. The material is given in two parallel streams.

Book: Differential Geometry of Curves and Surfaces: A Concise Guide