This volume covers local as well as global differential geometry of
curves and surfaces.
makes extensive use of elementary linear algebra with
emphasis on basic geometrical facts rather than on machinery or random
stresses the basic ideas of differential geometry
regular surfaces, the Gauss map, covariant derivatives.
includes a large number of fully-worked examples.
1. Curves: Parametrized Curves.
2. Regular Surfaces: Regular Surfaces; Inverse Images
of Regular Values.
3. Geometry of the Gauss Map: Definition of the Gauss
Map and Its Fundamental Properties.
4. Intrinsic Geometry of Surfaces: Isometrics; Conformal
5. Global Differential Geometry: Rigidity of the Sphere.