The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


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Paper's Title:

Sweeping Surfaces with Darboux Frame in Euclidean 3-space E3


F. Mofarreh, R. Abdel-Baky and N. Alluhaibi

Mathematical Science Department, Faculty of Science,
Princess Nourah bint Abdulrahman University
Riyadh  11546,
Saudi Arabia.

Department of Mathematics, Faculty of Science,
University of Assiut,
Assiut 71516,

Department of Mathematics Science and Arts, College Rabigh Campus,
 King Abdulaziz University
Saudi Arabia.


The curve on a regular surface has a moving frame and it is called Darboux frame. We introduce sweeping surfaces along the curve relating to the this frame and investigate their geometrical properties. Moreover, we obtain the necessary and sufficient conditions for these surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced.

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