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Indian Institute of Science Education and Research Bhopal

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

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