Comprehensive Study of Curves in Differential Geometry

ISBN-13: 9783659874079 / Angielski / Miękka / 2016 / 224 str.

Sahar Mohamed Ali Abou Bakr

Opis

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, binormals,tangent 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 frame,a 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, exercises,and problem solving to meet the quality standard.

O autorze

Sahar Mohamed Ali is an associate professor of pure mathematics at Ain Shams University, Faculty of Science, Cairo, Egypt, teaches some pure mathematical courses for under graduate and post graduate students, supervising projects, M.Sc and Ph.D thesis, authoring many research papers and books, her major field of study is functional & real Analysis