Riemannian geometry: a beginner's guide/ Frank Morgan

Includes bibliography and index

Preface -- Introduction -- Curves in R^n -- Surfaces in R^3 -- Surfaces in R^n -- m-Dimensional surfaces in R^n -- Intrinsic Riemannian geometry -- General relativity -- The Gauss-Bonnet theorem -- Geodesics and global geometry -- General norms

This classic text serves as a tool for self-study; it is also used as a basic text for undergraduate courses in differential geometry. The author's ability to extract the essential elements of the theory in a lucid and concise fashion allows the student easy access to the material and enables the instructor to add emphasis and cover special topics. The extraordinary wealth of examples within the exercises and the new material, ranging from isoperimetric problems to comments on Einstein's original paper on relativity theory, enhance this new edition.