| 书目名称 | Metric Structures in Differential Geometry |
| 编辑 | Gerard Walschap |
| 视频video | |
| 概述 | Includes supplementary material: |
| 丛书名称 | Graduate Texts in Mathematics |
| 图书封面 |  |
| 描述 | This text is an elementary introduction to differential geometry. Although it was written for a graduate-level audience, the only requisite is a solid back ground in calculus, linear algebra, and basic point-set topology. The first chapter covers the fundamentals of differentiable manifolds that are the bread and butter of differential geometry. All the usual topics are cov ered, culminating in Stokes‘ theorem together with some applications. The stu dents‘ first contact with the subject can be overwhelming because of the wealth of abstract definitions involved, so examples have been stressed throughout. One concept, for instance, that students often find confusing is the definition of tangent vectors. They are first told that these are derivations on certain equiv alence classes of functions, but later that the tangent space of ffi.n is "the same" n as ffi. . We have tried to keep these spaces separate and to carefully explain how a vector space E is canonically isomorphic to its tangent space at a point. This subtle distinction becomes essential when later discussing the vertical bundle of a given vector bundle. |
| 出版日期 | Textbook 2004 |
| 关键词 | Immersion; Riemannian geometry; Submersion; Tensor; curvature; differential geometry; manifold |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-0-387-21826-7 |
| isbn_softcover | 978-1-4419-1913-7 |
| isbn_ebook | 978-0-387-21826-7Series ISSN 0072-5285 Series E-ISSN 2197-5612 |
| issn_series | 0072-5285 |
| copyright | Springer Science+Business Media New York 2004 |
发表于 2025-3-21 19:51:58
