MA 233: Differential Geometry
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:
do Carmo, M. P., Differential Geometry of curves and surfaces
Thorpe, J. A., Elementary topics in Differential Geometry
,Springer-Verlag (UTM), 1979.
O'Neill, B., Elementary Differential Geometry
Gray, A., Modern Differential Geometry of Curves and Surfaces
,CRC Press, 1993.
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