Contents

• Introduction
• The continuous
  • Basic differential geometry
    • Definitions for curves
    • Parameterizing a curve by arc length
    • Curvature of curves
    • Regular surfaces
    • Tangent plane and surface normal
    • First fundamental form
    • Gauss map
    • Normal curvature
    • Second fundamental form (shape operator)
    • Principal curvatures
    • Mean and Guassian curvatures
    • Classification of surface points
    • Expressions for curvature of parametric surfaces
    • Gauss-Bonnet theorem
    • One-forms
    • Closed forms
    • Stokes theorem
  • Deformable surface models
    • Linear elasticity
  
  
• Further reading
• Differential of a map
• Bibliography