Requiring only an understanding of differentiable manifolds, Isaac Chavel covers introductory ideas followed by a selection of more specialized topics in this second edition. He provides a clearer treatment of many topics, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. Among the classical topics shown in a new setting is isoperimetric inequalities in curved spaces. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.
Review
"Each chapter concludes with an excellent section of notes and advanced exercises with further results, with hints and sketches of solutions at the end of the book...I think that it is the best reference on Riemannian geometry available, especially for someone interested in isoperimetric problems...Chavel is one of about a dozen mathematics books I keep at home for ready reference."
Frank Morgan, SIAM Review Read more...
