| 书目名称 | Curves and Surfaces | | 编辑 | Marco Abate,Francesca Tovena | | 视频video | http://file.papertrans.cn/242/241555/241555.mp4 | | 概述 | Includes supplementary material: | | 丛书名称 | UNITEXT | | 图书封面 |  | | 描述 | The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of1-dimensional manifolds. We then present the classical local theory of parametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenet’s formulas and the fundamentaltheorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves.The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivation | | 出版日期 | Textbook 2012 | | 版次 | 1 | | doi | https://doi.org/10.1007/978-88-470-1941-6 | | isbn_softcover | 978-88-470-1940-9 | | isbn_ebook | 978-88-470-1941-6Series ISSN 2038-5714 Series E-ISSN 2532-3318 | | issn_series | 2038-5714 | | copyright | Springer-Verlag Milan 2012 |
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