Since the times of Gauss, Riemann, and Poincaré, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching ...(展开全部)

Since the times of Gauss, Riemann, and Poincaré, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching ...(展开全部)

This volume covers local as well as global differential geometry of curves and surfaces. *Makes extensive use of elementary linear algebra - with emphasis on basic geometrical facts rather than on machinery or random details. *Stresses the basic ideas of differential geometry - regular surfaces, the Gauss map, covariant derivatives. *Includes a large number of fully-work...(展开全部)

This set features: "Foundations of Differential Geometry, Volume 1 " (978-0-471-15733-5) and "Foundations of Differential Geometry, Volume 2" (978-0-471-15732-8), both by Shoshichi Kobayashi and Katsumi Nomizu

One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises e...(展开全部)

Differential geometry has a long, wonderful history. It has found relevance in areas ranging from machinery design to the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses ...(展开全部)

Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum - nothing beyond first courses in linear algebra and multivariable calculus - and the most direct and straightforward approach is used throughout. New features of this revised and...(展开全部)

Andrew Pressley（1904-1988），伦敦国王学院的数学教授。Andrew是国际知名学者，在数学界享有盛誉，他的研究领域主要是数学物理与统计物理

An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory. Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables wh...(展开全部)