Differential Geometry

Curves

• Chapter 1.1 Basic Concepts
• Chapter 1.2 Arc Length
• Chapter 1.3 Tangent Line, Unit Tangent Vector, and Normal Plane
• Chapter 1.4 Osculating Plane
• Chapter 1.5 Normal Line and Principal Unit Normal Vector
• Chapter 1.6 Curvature and Osculating Circle
• Chapter 1.7 Binormal Vector, Binormal Line, and Rectifying Plane
• Chapter 1.8 Torsion
• Chapter 1.9 Frenet-Serret Formulae
• Chapter 1.10 Vector of Darboux
• Chapter 1.11 Unit Spherical Indicatrices
• Chapter 1.12 Approximate Curves
• Chapter 1.13 Contact and Osculating Sphere

Surfaces

First Fundamental Form

Tensors

Second Fundamental Form

Geodesics

Mappings

Absolute Differentiation, Displacement

Special Surfaces