| 书目名称 | Fundamentals of Differential Geometry | | 编辑 | Serge Lang | | 视频video | | | 概述 | New edition of a successful Serge Lang title.Written in the authors unique and engaging style, with clear and elegant proofs.Covers the fundamentals of differential geometry, differential topology, an | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | The present book aims to give a fairly comprehensive account of the fundamentals of differential manifolds and differential geometry. The size of the book influenced where to stop, and there would be enough material for a second volume (this is not a threat). At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differen tiable maps in them (immersions, embeddings, isomorphisms, etc. ). One may also use differentiable structures on topological manifolds to deter mine the topological structure of the manifold (for example, it la Smale [Sm 67]). In differential geometry, one puts an additional structure on the differentiable manifold (a vector field, a spray, a 2-form, a Riemannian metric, ad lib. ) and studies properties connected especially with these objects. Formally, one may say that one studies properties invariant under the group of differentiable automorphisms which preserve the additional structure. In differential equations, one studies vector | | 出版日期 | Textbook 1999 | | 关键词 | Derivative; Riemannian geometry; Smooth function; calculus; curvature; differential equation; differential | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-0541-8 | | isbn_softcover | 978-1-4612-6810-9 | | isbn_ebook | 978-1-4612-0541-8Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer Science+Business Media New York 1999 |
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发表于 2025-3-21 16:59:59
