Includes bibliographical references (p. 467) and index.

Introduction

Chapter 1: calculus on euclidean space:
Euclidean space. Tangent vectors. Directional derivatives. Curves in r3. 1-forms. Differential forms. Mappings;

Chapter 2: frame fields:
Dot product. Curves. The frenet formulas. Arbitraryspeed curves. Covariant derivatives. Frame fields. Connection forms. The structural equations. ;

Chapter 3: euclidean geometry:
Isometries of r3. The tangent map of an isometry. Orientation. Euclidean geometry. Congruence of curves. ;

Chapter 4: calculus on a surface:
Surfaces in r3. Patch computations. Differentiable functions and tangent vectors. Differential forms on a surface. Mappings of surfaces. Integration of forms. Topological properties. Manifolds.;

Chapter 5: shape operators:
The shape operator of m r3. Normal curvature. Gaussian curvature. Computational techniques. The implicit case. Special curves in a surface. Surfaces of revolution. ;

Chapter 6: geometry of surfaces in r3:
The fundamental equations. Form computations. Some global theorems. Isometries and local isometries. Intrinsic geometry of surfaces in r3. Orthogonal coordinates. Integration and orientation. Total curvature. Congruence of surfaces. ;

Chapter 7: riemannian geometry: geometric surfaces. Gaussian curvature. Covariant derivative. Geodesics. Clairaut parametrizations. The gauss-bonnet theorem. Applications of gauss-bonnet. ;

Chapter 8: global structures of surfaces: length-minimizing properties of geodesics. Complete surfaces. Curvature and conjugate points. Covering surfaces. Mappings that preserve inner products. Surfaces of constant curvature. Theorems of bonnet and hadamard. ;

Appendix

Bibliography

Answers to odd-numbered exercises

Subject index