Classical differential geometry

Preface
Chapter 1. General Curve Theory
	1.1. Curves
	Exercises
	1.2. Arclength and Linear Motion
	Exercises
	1.3. Curvature
	Exercises
	1.4. Integral Curves
	Exercises
Chapter 2. Planar Curves
	2.1. The Fundamental Equations
	Exercises
	2.2. The Rotation Index
	Exercises
	2.3. Three Interesting Results
	Exercises
	2.4. Convex Curves
	Exercises
Chapter 3. Space Curves
	3.1. The Fundamental Equations
	Exercises
	3.2. Characterizations of Space Curves
	Exercises
	3.3. Closed Space Curves
	Exercises
Chapter 4. Basic Surface Theory
	4.1. Surfaces
	Exercises
	4.2. Tangent Spaces and Maps
	Exercises
	4.3. The First Fundamental Form
	Exercises
	4.4. Special Maps and Parametrizations
	Exercises
Chapter 5. Curvature of Surfaces
	5.1. Curves on Surfaces
	Exercises
	5.2. The Gauss and Weingarten Maps and Equations
	Exercises
	5.3. The Gauss and Mean Curvatures
	Exercises
	5.4. Principal Curvatures
	Exercises
	5.5. Ruled Surfaces
	Exercises
Chapter 6. Surface Theory
	6.1. Generalized and Abstract Surfaces
	Exercises
	6.2. Curvature on Abstract Surfaces
	Exercises
	6.3. The Gauss and Codazzi Equations
	Exercises
	6.4. The Gauss-Bonnet Theorem
	Exercises
	6.5. Topology of Surfaces
	Exercises
	6.6. Closed and Convex Surfaces
	Exercises
Chapter 7. Geodesics and Metric Geometry
	7.1. Geodesics
	Exercises
	7.2. Mixed Partials
	Exercises
	7.3. Shortest Curves
	Exercises
	7.4. Short Geodesics
	7.5. Distance and Completeness
	Exercises
	7.6. Isometries
	Exercises
	7.7. Constant Curvature
	7.8. Comparison Results
Chapter 8. Riemannian Geometry
Appendix A. Vector Calculus
	A.1. Vector and Matrix Notation
	A.2. Geometry
	A.3. Geometry of Space-Time
	A.4. Differentiation and Integration
	A.5. Differential Equations
Appendix B. Special Coordinate Representations
	B.1. Cartesian and Oblique Coordinates
	B.2. Surfaces of Revolution
	B.3. Monge Patches
	B.4. Surfaces Given by an Equation
	B.5. Geodesic Coordinates
	B.6. Chebyshev Nets
	B.7. Isothermal Coordinates
Bibliography