Differential Geometry of Curves and Surfaces(English, Paperback, Toponogov Victor Andreevich)

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Differential Geometry of Curves and Surfaces(English, Paperback, Toponogov Victor Andreevich) is written by Toponogov Victor Andreevich and published by Birkhauser Boston Inc. It's available with International Standard Book Number or ISBN identification 0817643842 (ISBN 10) and 9780817643843 (ISBN 13).

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 collection (80 to 90) ofnonstandard andoriginalproblems that introduce the student into the real world of geometry.