| 书目名称 | Differential Geometry of Curves and Surfaces | | 副标题 | A Concise Guide | | 编辑 | Victor A. Toponogov,Vladimir Y. Rovenski | | 视频video | | | 概述 | Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem.Many nontrivial and original problems (some with hints and solutions | | 图书封面 |  | | 描述 | This concise guide to the differential geometry of curves and surfaces can be recommended to ?rst-year graduate students, strong senior students, and students specializing in geometry. The material is given in two parallel streams. The ?rst stream contains the standard theoretical material on differential ge- etry of curves and surfaces. It contains a small number of exercises and simple problems of a local nature. It includes the whole of Chapter 1 except for the pr- lems (Sections 1.5, 1.7, 1.10) and Section 1.11, about the phase length of a curve, and the whole of Chapter 2 except for Section 2.6, about classes of surfaces, T- orems 2.8.1–2.8.4, the problems (Sections 2.7.4, 2.8.3) and the appendix (S- tion 2.9). The second stream contains more dif?cult and additional material and for- lations of some complicated but important theorems, for example, a proof of A.D. Aleksandrov’s comparison theorem about the angles of a triangle on a convex 1 surface, formulations of A.V. Pogorelov’s theorem about rigidity of convex s- faces, and S.N. Bernstein’s theorem about saddle surfaces. In the last case, the formulations are discussed in detail. A distinctive feature of the book is a large | | 出版日期 | Textbook 2006 | | 关键词 | Riemannian geometry; curvature; differential geometry; ksa; manifold | | 版次 | 1 | | doi | https://doi.org/10.1007/b137116 | | isbn_softcover | 978-0-8176-4384-3 | | isbn_ebook | 978-0-8176-4402-4 | | copyright | Birkhäuser Boston 2006 |
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发表于 2025-3-21 18:27:01
