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Document Type |
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Thesis |
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Document Title |
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On the curvature functions of ruled surfaces in Euclidean 3-Space عن دوال الإنحناء للسطوح المسطرة في الفضاء الإقليدي ثلاثي البعد |
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Subject |
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Faculty of Science |
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Document Language |
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Arabic |
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Abstract |
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In Chapter 1, we show some principles and basic concepts in the differentiation geometry that is necessary to complete the thesis, we have first presented in a brief picture and some of concepts related to the curves in Euclidean 3-space E3. We also presented the concepts of surfaces in Euclidean 3-space E3 and presented Darboux frame on the surface. We have introduced the ruled surface and its parametric equation. Further, we have presented a profound study about the developable ruled surfaces.
In Chapter 2, we have defined a ruled surface normal to a surface along a curve on the surface. Then, we analyze the necessary and sufficient condition for that surface to be normal developable. Also, we solve the problem when the resulting developable surface is a cylinder, cone or tangent surface. Finally, we illustrate some representative examples.
In Chapter 3, we define a ruled surface osculating to a surface along a curve on the surface. Then, we analyze the necessary and sufficient condition for that surface to be osculating developable. Moreover, we solve the problem when the resulting developable surface is a cylinder, cone or tangent surface. Also, we illustrate the convenience and efficiency of this approach by some representative examples.
In Chapter 4, we intrdouce Bertrand offsets of ruled surfaces with Darboux frames in Euclidean 3-space E3. Geometric characterizations of these ruled surfaces as the striction curve, distribution parameter and orthogonal trajectories are investigated. In particular, we have calculated the relationships between the characteristic properties of the ruled surfaces which are generated by the Darboux frames. Finally, we give some representative examples. |
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Supervisor |
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Prof. Rashad Abdel-Star Abdel-Baqi |
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Thesis Type |
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Doctorate Thesis |
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Publishing Year |
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1441 AH
2020 AD |
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Co-Supervisor |
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Prof. Reem Abdul Hamid Al-Ghafari |
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Added Date |
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Monday, June 8, 2020 |
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Researchers
| سحر حسين نازره | Nazerah, Sahar Hussein | Researcher | Doctorate | |
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