Basic differential geometry

This section follows do Cormo's Differential Geometry of Curves and Surfaces [do Cormo, 1976] closely, but focusses on local properties of curves and surfaces.

- 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

Copyright © 2005 Adrian Secord. All rights reserved.