Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

MA 233: Differential Geometry

Credits: 3:0

Curves in Euclidean space: Curves in R3, Tangent vectors, Differential derivations, Principal normal and binomial vectors, Curvature and torsion, Formulae of Frenet.

Surfaces in R3: Surfaces, Charts, Smooth functions, Tangent space, Vector fields, Differential forms, Regular Surfaces, The second fundamental form, Geodesies, Parellel transport, Weingarten map, Curvatures of surfaces, Rules surfaces, Minimal surfaces, Orientation of surfaces.    

Suggested books and references:

1. do Carmo, M. P., Differential Geometry of curves and surfaces, Prentice-Hall, 1976.
2. Thorpe, J. A., Elementary topics in Differential Geometry, Springer-Verlag (UTM), 1979.
3. O'Neill, B., Elementary Differential Geometry, Academic, 1996.
4. Gray, A., Modern Differential Geometry of Curves and Surfaces, CRC Press, 1993.

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