Differential Geometry of Curves and Surfaces

A Concise Guide
Buch | Softcover
206 Seiten
2005
Birkhauser Boston Inc (Verlag)
978-0-8176-4384-3 (ISBN)
74,89 inkl. MwSt
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.

From the reviews:"This book by the late author covers … the subjects which are normally taught in a course on the differential geometry of curves and surfaces. … It can be recommended for first-year graduate students and also for use in the classroom. … the book is rich in geometry and concrete examples. … the book is very welcome since it is an original contribution in various aspects and gives a number of geometric insights … . Numerous illustrations make the reading enjoyable." (Wolfgang Kühnel, Mathematical Reviews, Issue 2006 m)"Toponogov’s ‘concise guide’ to elementary differential geometry has the potential to be a useful reference and/or review book … ."(Fernando Q. Gouvèa, MathDL, March, 2006)“This book, written by one of the Russian masters, offers a comprehensive introduction to classical differential geometry of curves and surfaces. Only a basic background in analysis and linear algebra is needed to follow the presentation. … A distinctive feature of the book is that, apart from a large number of exercises, it also contains many original problems with outlines of solutions.” (A. Cap, Monatshefte für Mathematik, Vol. 155 (1), September, 2008)

Erscheint lt. Verlag 5.12.2005
Mitarbeit Assistent: Vladimir Rovenski
Zusatzinfo 70 Illustrations, black and white; XIV, 206 p. 70 illus.
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
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