e10fea2a-7902-4fe3-ad38-9ab4a11eddcb20210507021923931wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40513220213220212010.37394/23206.2021.20https://wseas.org/wseas/cms.action?id=23278Sweeping surface of center curve on surface in Euclidean 3-space E³Rashad A.Abdel-BakyDepartment of Mathematics; Faculty of Science, University of Assiut, Assiut 71516; EgyptFatemahMofarrehMathematical Sciencedepartment; Faculty of Science; Princess Nourah Bint Abdulrahman University, Riyadh 11546, Saudi ArabiaFor the curve on the regular surface, there is moving frame with this thatis named Darboux frame. Sweeping surfaces through the curve associated with Darboux frame are introduced and their geometrical properties are investigated. Moreover, we obtain the necessary and sufficient conditions of this kind of surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced.572021572021235243https://www.wseas.org/multimedia/journals/mathematics/2021/a485106-1324.pdf10.37394/23206.2021.20.24https://www.wseas.org/multimedia/journals/mathematics/2021/a485106-1324.pdfMP. Do Carmo. Differential Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, NJ, 1976. 10.1016/s0940-9602(01)80067-4B. Yildiz, K. Arslan, H. Yildiz, C. Ozgur. A geometric description of the ascending colon of some domestic animals. Ann Anat, vol.183, No.6, 2001, pp 555-557. PA. Blaga. On tubular surfaces in computer graphics. Stud Univ Babes-Bolyai In- form, 2005, pp 81-90. W. Wang, B. Juttler, D. Zheng & Y. Liu. Computation of rotating minimizing frames. ACM Transactions on Graphics,vol. 27, No.1, 2008, pp 1-18. MK. Karacan, Y. Yayli. On the geodesics of tubular surfaces in Minkowski 3-space. Bull Malays Math Sci Soc; vo;.31, No.1, 2008, pp 1-10. 10.1016/j.jsc.2010.03.004RT. Farouki & T. Sakkalis. Rational rotationminimizing frames on polynomial space curves of arbitrary degree,. J Symb Com- put,vol. 45, No.8, 2010, pp 844{856. 10.1155/2011/191849Karacan MK, Yoon DW, Tuncer Y. Weingarten and linear Weingarten type tubular surfaces in E3 . Math Prob in Eng 2011, doi. no: 10.1155/2011/191849. F. Doggan. Generalized Canal Surfaces. PhD, Ankara University Graduate School, Ankara, Turkey, 2012. 10.1007/s00006-015-0602-5S. Aslan, Y. Yayli. Canal surfaces with quaternions. Adv Appl Clifford Algebras; vol. 26No.1, 2015, pp 31-38. 10.1007/s00006-016-0703-9I Gok. Quaternionic approach of canal surfaces constructed by some new ideas. Adv in Appl Clifford Algebras, vol.27, No.2, 2017, pp 1-16. RA. Abdel-Baky & Y. Ynluturk. On the curvatures of spacelike circular surface, Kuwait Journal of Science, vol. 43, Vol.3, 2016. 10.1002/mma.5574H. Shichang, W. Zhigang & T. Xiaoqing. Tubular surfaces of center curves on spacelike surfaces in Lorentz-Minkowski 3-space, Math Meth Appl Sci, 2018, pp1{31. 10.1142/s0219887820500747RA. Abdel-Baky, N. Alluhaibi, A. Ali & F. Mofarreh. A study on timelike circular surfaces in Minkowski 3-Space. Int. J. of Geometric Methods in Modern Physics, vol. 17, No. 06, 2020. 10.1007/s41980-018-0177-8RA. Abdel-Baky. Developable surfaces through sweeping surfaces, Bulletin of the Iranian Mathematical Society, Vol. 45, no. 4, 2019, pp 951{963. 10.1016/j.pnsc.2007.09.001H.Y. Zhao, and G.J. Wang. A new method for designing a developable surface utilizing the surface pencil through a given curve. Progress in Nature Science, vol. 18, 2008, pp 105{10. 10.1016/j.cad.2012.11.001C.Y. Li, R.H. Wang, and C.G. Zhu. An approach for designing a developable surface through a given line of curvature, Computer- Aided Design, vol. 45, 2013, pp 621{627. 10.1007/s13373-014-0063-5O.G Yildiz, S.O. Karakus, and H.H. Hacisalihoglu. On the determination of a developable spherical orthotomic ruled surface, Bull. Math. Sci. vol. 5, 2015, pp 137{146. 10.22342/jims.26.3.872.319-333R.A. Abdel-Baky & Y. Unluturk. Normal developable surfaces of a surface along a space curve, J. Indones. Math. Soc. Vol. 26, No. 03,2010, pp. 319-333. 10.37394/23206.2020.19.61R.A. Abdel-Baky & F. Mofarreh. On the determination of ruled and developable surfaces in Euclidean 3-space, WSEAS Transactions on Mathematics DOI: 10.37394/23206.19.60, (2020). 10.22541/au.158480062.28684138R.A. Abdel-Baky & Y. Unluturk. A new construction of timelike ruled surfaces with constant Disteli-axis, Honam Math. Journal,vol. 42, No. 3,2020, pp. 551-568.