Differential Geometry of Curves and Surfaces : A Concise Guide PDF

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.