الفهرس 
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Abstract
This thesis is interested in studying dual spherical curves, the corresponding
ruled surfaces and some special types of dual curves and ruled surfaces.
This thesis consists of five main chapters and a list of references and detailed
as follows:
Chapter I: In this chapter we survey the concept of dual calculus and its
representation as a field of numbers corresponding to the field of real numbers.
Also, the dual unit sphere and the dual space curve are given. Finally, the dual
Bishop frame and dual Darboux frame are defined.
Chapter II: This chapter contains a study of two kinds of curves in Dual space.
We considered spherical motion of each curve with its tangent, normal,
binormal and Darboux lines and present the analysis of this motion with Bishop
frame in three-dimensional dual space D3
. We obtained some important results.
Chapter III: This chapter comprised of the study of another type of curves
(dual focal curves) in terms of their Bishop focal curvatures. The evolution
equations of the Bishop frame and the curvatures of these curves were given.
Chapter IV: This chapter deals with the study of an important type of curves
known as (dual Arslan West curves (i.f. DAW(k) curves of type k (1≤k≤3)) on
a dual unit sphere and give some relationships between the Bishop curvatures
of these curves. Also, we investigate some special curves such as slant helices,
evolute curves and normal curves of Bishop DAW(k)-type, and we got some
important theorems for these curves and support these results with some
examples.
Chapter V: This chapter aims at studying some special types of dual ruled
surfaces associated to the dual focal curves. Moreover, the inextensibility of
each ruled surface is studied. Furthermore, necessary conditions for