Differential Geometry of Curves and Surfaces
A Concise Guide
Seiten
2005
|
2006 ed.
Birkhauser Boston Inc (Verlag)
978-0-8176-4384-3 (ISBN)
Birkhauser Boston Inc (Verlag)
978-0-8176-4384-3 (ISBN)
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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.
Theory of Curves in Three-dimensional Euclidean Space and in the Plane.- Extrinsic Geometry of Surfaces in Three-dimensional Euclidean Space.- Intrinsic Geometry of Surfaces.
| Erscheint lt. Verlag | 5.12.2005 |
|---|---|
| Mitarbeit |
Assistent: Vladimir Rovenski |
| Zusatzinfo | 70 Illustrations, black and white |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-8176-4384-2 / 0817643842 |
| ISBN-13 | 978-0-8176-4384-3 / 9780817643843 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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