Comprehensive Study of Curves in Differential Geometry

The topics of this textbook are curves in differential geometry and they are primarily studied by means of parametrization. Particularly; curvilinear coordinates plane curves and skew curves like; helices involutes evolutes spherical indicatrix circles and spheres of curvatures. It also introduces some quadratic surfaces theory of contacts curves-surfaces contacts relationships envelops the geometry of curves in differential geometry in general. The main properties of these objects which will be studied are notions related to the shape;tangents principle normals binormalstangent lines normal planes osculating planes and rectifying planes. The fundamental investigated concepts are curvatures and torsion as the basic intrinsic property of a curve independent of its isometric embedding in Euclidean space. One of the most important tools used to analyze a curve is the Serret-Frenet framea moving frame that provides a coordinate system at each point of the curve that is best adapted to the curve near that point.This text is supplied with sufficient illustrated figures adequate number of examples exercisesand problem solving to meet the quality standard.