Differential Geometry of Curves and Surfaces : MTH 406

Grading Policy

Homeworks: 10%
Quizzes/Presentations: 10%
Mid semester exam: 30%
End semester exam: 50%

Schedules

Class : Wednesday, Thursday and Friday 10:00-11:00 Hrs.

Course contents

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

Homeworks

Quizzes

Exams

Reference texts for the course

Montiel and Ross, Curves and Surfaces, Graduate Studies in Mathematics, Vol. 69, AMS (Indian Edition), 2011.

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