Mathematics

**MTH ****406: Differential Geometry of Curves and Surfaces**** ****(4)**

**Pre-requisites**: MTH 306 Ordinary Differential Equations

Curves: curves in space, tangent vector, arc length, curvature, torsion, Frenet formulas

Surfaces: parametrization, tangent plane, orientability, first fundamental form, area, orientation, Gauss map, second fundamental form, Gauss curvature, ruled and minimal surfaces

Geodesics, isometries of surfaces, Gauss’ Theorema Egregium, Codazzi-Mainardi equations

Gauss-Bonnet theorem for compact surfaces

*Suggested Books*:

- Pressley,
*Elementary Differential Geometry*, Springer, Indian reprint, 2004 - Manfredo do Carmo,
*Differential Geometry of Curves and Surfaces*, Prentice Hall, 1976 - D. J. Struik,
*Lectures on Differential Geometry*, Dover, 1988 - Barrett O’Neill,
*Elementary Differential Geometry*, Second edition, Academic Press (Elsevier), 2006

Previous | Back to Course List | Next |