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