Login

Differential Geometry Description

Key Elements

Code

MATH 308

Formation

BS Mathematics

Semester

6

Credits

6

Number of Teaching Hours

30

Number of Tutoring Sessions

30

Number of Laboratory Sessions

0

Content

Objective

Initiate the study of the differential geometry using the study of curves and surfaces in R3.

Content

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.