الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Curves in semi-Riemannian manifold especially in Minkowski 3-space is one of the interesting topics in the differential geometry. In fact, a lot of mathematicians such as [ ] have paid a great deal of interests toward such topics. Therefore, this thesis focused mainly on the study of such area of research. Moreover, these kinds of scientific fields are still need of more of studies. This thesis interested in studying some geometric properties of some curves such as Bertrand, Evolute and Involute curves. In addition, generalizations of above curves in Minkowski space were studied in different frames such as the Equiform frame and the modified orthogonal frame. Also, some of the characteristics and theorems of the helix were generalized according to the modified orthogonal frame in Minkowski 3-space. Finally, we presented some practical examples for the results of this study. This thesis consists of four chapters which contains the results we have established. Chapter 1, presented the basic concepts in differential geometry that were relied upon in this study. Especially, the notions of smooth manifold, vector field, metric tensor, Riemannian and semi-Riemannian manifolds. Also, we introduced the Lorentz Minkowski 3-space and curves in Minkowski 3-space. In Chapter 2, we introduced some examples of curves in Minkowski 3-space such as Bertrand, Evolute, Helix, Mannheim and Involute curves. Especially, some of the characteristics, theorems and results related to the xi general and slant helices. Finally, we presented some results of previous studies of the curves which were used later in this study. In Chapter 3, we present the equiform frame of some curves in Minkowski 3-space and the principal normal curves in the case of equiform spacelike curves. This chapter consists of an introduction, the preliminaries and three sections as follows: Section 3.3, includes the definitions of an equiform parameter and equiform frame in Minkowski 3-space. Moreover, we introduce an equiform frame and equiform formulas for the involute curve in the case of an equiform spacelike curve with a spacelike equiform principal normal. Section 3.4, we studied the principal normal for the evolute curve in the case of an equiform spacelike curve with a spacelike equiform principal normal Minkowski 3-space. In addition, some results of this curve are presented. The main results of this chapter have been accepted in “Ciencia Tecnica Vitivinicola Journal” in 2019 under the title “Involute and Evolute Curves According to the Equiform Frame in Minkowski 3-space ” . Section 3.5, includes examples of equiform spacelike curves in Minkowski 3-space and satisfy the theorems and corollaries that discussed in sections 3.3 and 3.4. In Chapter 4, the modified orthogonal frame and some curves in Minkowski 3-space were generalized under the influence of this frame. This chapter was divided into an introduction, the preliminaries and four sections as follows: xii In Section 4.3, we investigate the involute curve according to the modified orthogonal frame in Minkowski 3-space. In Section 4.4, we introduce some characteristics and theorems for the general and slant helices with the modified orthogonal frame in Minkowski 3-space. In Section 4.5, includes examples of involute and helix curves according to the modified orthogonal frame in Minkowski 3-space and satisfy the theorems that discussed in sections 4.3 and 4.4. The main results of sections 4.3 and 4.4 have been published as an independent paper under the title ”On Some Special Curves According to the Modified Orthogonal Frame in Minkowski 3-Space ” in KASMERA journal Vol. 49 (No 6, 2021). In Section 4.6, we study Bertrand curves according to the modified orthogonal frame in Minkowski 3-space and some examples are presented. The main results of section 4.6 have been published as an independent paper under the title ”Bertrand Curves with the Modified Orthogonal Frame in Minkowski 3-space”. In REVISTA DE EDUCATION Vol. 392 (No 6, 2021).