Differential Geometry - 9780821839881

Writing for undergraduates with courses in analysis and linear algebra, Kuhnel works carefully and logically through his chapters, giving newcomers a summary of the prerequisite analysis and moving directly to curves, including plane curves and space curves, Frenet curves, and curves in Minkowski space, the local theory of surfaces, including surface elements, first fundamental form, the Gauss map and the curvature of surfaces, surfaces of rotation and rules surfaces, minimal surfaces and surfaces in Minkowski space, the intrinsic geometry of surfaces, including the covariant derivative, the Gaussian equation and the Theorema Egregium, and the Gauss-Bonnet theorem, Riemann manifolds, including the tangent space and the Reimannian connection, the curvature tensor, including the Ricci and Einstein tensors, spaces of constant curvature, including geodesics and Jacobi fields, and Einstein spaces, including the decomposition of the curvature tensor and the Weyl tensor. The text is clearly and carefully illustrated. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)