Initiate the study of the differential geometry using the study of curves and surfaces in R3.
1. Affine space, Euclidian case.
2. Curves in Rn – parametrization – orientation – tangent .
3. Curves in R2 and R3, curvature, torsion, Frenet’s frame.
4. Global properties of curves.
5. Parametric surfaces in R3, orientation, tangent plane, normal.
6. First fundamental form : length, area of a surface.
7. Curvature of surfaces: Second fundamental form, curvature of a curve in a surface, Geometric Interpretation of the principal curvature.
8. Geodesics: Equations, case of the surfaces of revolution, geodesics coordinates.
9. Minimal surfaces: Definition, Examples.