Differential Geometry of Curves and Surfaces
Shiing-Shen Chern, Thomas Banchoff, and William Pohl

II: Curves

2.1. Arc Length
2.2. Curvature and Fenchel's Theorem
2.3. The Unit Normal Bundle and Total Twist
2.4. Moving Frames
2.5. Non-Inflectional Curves and the Frenet Formulas
2.6. Local Equations of a Curve

III: Fundamental Forms of a Surface

3.1.1 The First Fundamental Form
3.1.2. Geometry in the Tangent Plane
3.2.1. The Second Fundamental Form
3.2.2. The Shape of a Surface
3.2.3. Characterization of the Sphere
3.2.4. Principal Curvatures, Principal Directions, and Lines of Curvature
3.2.5. Gauss Mapping and the Third Fundamental Form

IV: Fundamental Equations of Surface Theory, Congruence Theorem

4.1. Weingarten and Gauss Equations
4.2. Levi-Civita Parallelism
4.3. Integrability Conditions
 Differential Geometry Laboratories
Thomas Banchoff and Associates

Lab 1. Local Theory of Plane Curves

Lab 2. More Local Theory of Plane Curves

Lab 3. Local Theory of Space Curves

Lab 4. Theory of Space Curves, Continued

Lab 5. Local Theory of Surfaces

Demo Software Documentation


Old Labs