| 书目名称 | Introduction to Differential Geometry | | 编辑 | Joel W. Robbin,Dietmar A. Salamon | | 视频video | | | 概述 | Differential Geometry from an extrinsic and an intrinsic view point.One semester lecture course for students of mathematics or STEM disciplines.Contains a lot of examples and exercises | | 丛书名称 | Springer Studium Mathematik (Master) | | 图书封面 |  | | 描述 | This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point..The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor...An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson‘s differential geometric approach to Lie algebra t | | 出版日期 | Textbook 2022 | | 关键词 | extrinsic differential geometry; extrinsic vs; intrinsic differential geometry; accessible differentia | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-662-64340-2 | | isbn_softcover | 978-3-662-64339-6 | | isbn_ebook | 978-3-662-64340-2Series ISSN 2509-9310 Series E-ISSN 2509-9329 | | issn_series | 2509-9310 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE |
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发表于 2025-3-21 18:05:25
