Differential Geometry: Handwritten notes - … erential Geometry: Handwritten notes by Prof.(Rtd)...
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Differential Geometry: Handwritten notes
by
Prof.(Rtd) Muhammad Saleem
Department of Mathematics,
University of Sargodha, Sargodha
Keywords
Curves with torsion:
Curve, space curve, equation of tangent, normal plane, principal normal curvature, deriva-
tion of curvature, plane of the curvature or osculating plane, principal normal or binormal,
rectifying plane, equation of binormal, torsion, Serret Frenet formulae, radius of torsion,
the circular helix, skew curvature, centre of circle of curvature, spherical curvature, locus of
centre of spherical curvature, helices, spherical indicatrix, evolute, involute.
Differential geometry of surfaces:
Surface, tangent plane and normal, equation of tangent plane, equaiton of normal, one pa-
rameter family of surfaces, characteristic of surface, envelopes, edge of regression, equation of
edge of regression, developable surfaces, osculating developable, polar developable, rectifying
developable.
Available at http://www.MathCity.org/msc
It is highly recommended that DON’T use these notes as a reference.
Reference: C. E. Weatherburn, Differential geometry of three dimensions, Cambridge at the
university press, 1955. ( http://archive.org/details/differentialgeom003681mbp )
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