Differential Geometry of Curves and Surfaces: A Concise Guide presents traditional material in classicial differential geometry 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.

The work covers central concepts including curves, surfaces, geodesics, intrinsic geometry, the Aleksandrov global angle comparison theorem, and the celebrated Toponogov Comparison Theorem . This rigorous exposition, with well-motivated topics and many nontrivial and original problems (some with hints and solutions), is ideal for advanced undergraduate and first-year graduate students seeking to enter the fascinating world of geometry.

Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem 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

Autorentext
Differential Geometry of Curves and Surfaces: A Concise Guide presents traditional material in classicial differential geometry 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.
The work covers central concepts including curves, surfaces, geodesics, intrinsic geometry, the Aleksandrov global angle comparison theorem, and the celebrated Toponogov Comparison Theorem . This rigorous exposition, with well-motivated topics and many nontrivial and original problems (some with hints and solutions), is ideal for advanced undergraduate and first-year graduate students seeking to enter the fascinating world of geometry.

Klappentext

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.

Inhalt
Theory of Curves in Three-dimensional Euclidean Space and in the Plane.- Extrinsic Geometry of Surfaces in Three-dimensional Euclidean Space.- Intrinsic Geometry of Surfaces.