Differential Geometry of Curves and Surfaces

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 author introduces the reader to curves, then progresses to surfaces and finally to more complex topics in the concluding section. The book weaves together standard theoretical material with more difficult theorems and complex problems while maintaining an easy separation between the two. One of the striking features of this presentation is the large number of non-trivial and original problems, some with useful hints and solutions, which introduce a motivated student into the real world of geometry. Another strong point is the non-trivial material connected with the Aleksandrov global angle comparison theorem. Its generalization for Riemannian spaces of arbitrary dimension is known as the celebrated Toponogov comparison theorem - one of the cornerstones of modern Riemannian geometry. This rigorous exposition, with well-motivated topics, is ideal for advanced undergraduate students, and first year graduate students.