| 书目名称 | Riemannian Manifolds | | 副标题 | An Introduction to C | | 编辑 | John M. Lee | | 视频video | | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | This book is designed as a textbook for a one-quarter or one-semester graduate course on Riemannian geometry, for students who are familiar with topological and differentiable manifolds. It focuses on developing an intimate acquaintance with the geometric meaning of curvature. In so doing, it introduces and demonstrates the uses of all the main technical tools needed for a careful study of Riemannian manifolds. The author has selected a set of topics that can reasonably be covered in ten to fifteen weeks, instead of making any attempt to provide an encyclopedic treatment of the subject. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics,without which one cannot claim to be doing Riemannian geometry. It then introduces the Riemann curvature tensor, and quickly moves on to submanifold theory in order to give the curvature tensor a concrete quantitative interpretation. From then on, all efforts are bent toward proving the four most fundamental theorems relating curvature and topology: the Gauss–Bonnet theorem (expressing the total curvature of a surface in term so fits topological type), the Cartan–Hadamard theorem (restricting the topolog | | 出版日期 | Textbook 19971st edition | | 关键词 | Riemannian geometry; Tensor; Volume; curvature; manifold | | 版次 | 1 | | doi | https://doi.org/10.1007/b98852 | | isbn_ebook | 978-0-387-22726-9Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer Science+Business Media New York 1997 |
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发表于 2025-3-21 16:27:04
