| 书目名称 | Smooth Manifolds | | 编辑 | Claudio Gorodski | | 视频video | | | 概述 | Presents the essence of the theory on smooth manifolds.Covers key topics such as submanifolds, tensor fields, Lie groups, integration (including Stokes’ theorem and De Rham cohomology), as well as man | | 丛书名称 | Compact Textbooks in Mathematics | | 图书封面 |  | | 描述 | This concise and practical textbook presents the essence of the theory on smooth manifolds. A key concept in mathematics, smooth manifolds are ubiquitous: They appear as Riemannian manifolds in differential geometry; as space-times in general relativity; as phase spaces and energy levels in mechanics; as domains of definition of ODEs in dynamical systems; as Lie groups in algebra and geometry; and in many other areas. The book first presents the language of smooth manifolds, culminating with the Frobenius theorem, before discussing the language of tensors (which includes a presentation of the exterior derivative of differential forms). It then covers Lie groups and Lie algebras, briefly addressing homogeneous manifolds. Integration on manifolds, explanations of Stokes’ theorem and de Rham cohomology, and rudiments of differential topology complete this work. It also includes exercises throughout the text to help readers grasp the theory, as well as more advanced problems for challenge-oriented minds at the end of each chapter. Conceived for a one-semester course on Differentiable Manifolds and Lie Groups, which is offered by many graduate programs worldwide, it is a valuable resour | | 出版日期 | Textbook 2020 | | 关键词 | smooth manifold; Lie groups; differential topology; Tensor analysis; differential geometry | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-49775-0 | | isbn_softcover | 978-3-030-49774-3 | | isbn_ebook | 978-3-030-49775-0Series ISSN 2296-4568 Series E-ISSN 2296-455X | | issn_series | 2296-4568 | | copyright | Springer Nature Switzerland AG 2020 |
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发表于 2025-3-21 19:24:59
