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An Examination on the Striction Curves in Terms of Special Ruled Surfaces

Year 2020, Volume: 5 Issue: 2, 118 - 123, 31.10.2020

Abstract

In this paper, we firstly express ruled surfaces drawn by Frenet
and Darboux vector fields of Bertrand mate curves depending on the Bertrand curve, which are called Bertrandian Frenet Ruled surfaces . Further the striction curves on these eigth special Frenet ruled surfaces have been calculated with a matrix representation . Then, the tangent vectors of the striction curves on these eigth special Frenet ruled surfaces are calculated with a matrix representation .
Finally, we give some results with these vectors.

References

  • Ergüt M., Körpınar T., Turhan E., On Normal Ruled Surfaces of General Helices In The Sol Space Sol3, TWMS J. Pure Appl. Math., 4(2013), 125-130.
  • Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton FL: CRC Press, 205, 1997. Hacısaliho˘glu H.H., Differential Geometry, In¨on¨u University publications, 1994.
  • Izumiya, S., Takeuchi, N., Special curves and Ruled surfaces, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry, 44(1)(2003), 203-212.
  • Kasap, E., Kuruoglu, N., The Bertrand offsets of ruled surfaces in R1 3, Acta Math. Vietnam, 31(1)(2006), 39-48.
  • Keçilioğlu, O., and ˙Ilarslan, K., Quaternionic Bertrand Curves in Euclidean 4-Space, Bulletin of Mathematical Analysis & Applications, 5(3)(2013), 27-38
  • Kılıçoğlu S¸, Senyurt S., Çalıskan A., On the striction curves along the involutive and Bertrandian Darboux ruled surfaces based on the tangent vector fields, New Trends in Mathematical Sciences, 4(4)(2016), 128-136.
  • Kılıçoğlu S¸, Senyurt S., Çalıskan A.,On the Tangent Vector Fields of Striction Curves Along the Involute and Bertrandian Frenet Ruled Surfaces, International Journal of Mathematical Combinatorics 2(2018), 33-43.
  • Kılıçoğlu S¸, Senyurt S., and Hacısaliho˘glu H.H., On the striction curves of Involute and Bertrandian Frenet ruled surfaces in E3, Applied Mathematical Sciences, 9(142) (2015), 7081 - 7094. http://dx.doi.org/10.12988/ams.2015.59606.
  • Monterde, J., The Bertrand curve associated to a Salkowski curve. Journal of Geometry, 111(2020), 1-16.
  • Şenyurt, S., Çalıskan, A., The quaternionic expression of ruled surfaces, Filomat, 32(16), (2018).
  • Şenyurt, S. and Kılıçoğlu S, On the differential geometric elements of the involute ˜D scroll, Adv. Appl. Clifford Algebras, 25(4)(2015), 977-988, doi:10.1007/s00006-015-0535-z.
Year 2020, Volume: 5 Issue: 2, 118 - 123, 31.10.2020

Abstract

References

  • Ergüt M., Körpınar T., Turhan E., On Normal Ruled Surfaces of General Helices In The Sol Space Sol3, TWMS J. Pure Appl. Math., 4(2013), 125-130.
  • Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton FL: CRC Press, 205, 1997. Hacısaliho˘glu H.H., Differential Geometry, In¨on¨u University publications, 1994.
  • Izumiya, S., Takeuchi, N., Special curves and Ruled surfaces, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry, 44(1)(2003), 203-212.
  • Kasap, E., Kuruoglu, N., The Bertrand offsets of ruled surfaces in R1 3, Acta Math. Vietnam, 31(1)(2006), 39-48.
  • Keçilioğlu, O., and ˙Ilarslan, K., Quaternionic Bertrand Curves in Euclidean 4-Space, Bulletin of Mathematical Analysis & Applications, 5(3)(2013), 27-38
  • Kılıçoğlu S¸, Senyurt S., Çalıskan A., On the striction curves along the involutive and Bertrandian Darboux ruled surfaces based on the tangent vector fields, New Trends in Mathematical Sciences, 4(4)(2016), 128-136.
  • Kılıçoğlu S¸, Senyurt S., Çalıskan A.,On the Tangent Vector Fields of Striction Curves Along the Involute and Bertrandian Frenet Ruled Surfaces, International Journal of Mathematical Combinatorics 2(2018), 33-43.
  • Kılıçoğlu S¸, Senyurt S., and Hacısaliho˘glu H.H., On the striction curves of Involute and Bertrandian Frenet ruled surfaces in E3, Applied Mathematical Sciences, 9(142) (2015), 7081 - 7094. http://dx.doi.org/10.12988/ams.2015.59606.
  • Monterde, J., The Bertrand curve associated to a Salkowski curve. Journal of Geometry, 111(2020), 1-16.
  • Şenyurt, S., Çalıskan, A., The quaternionic expression of ruled surfaces, Filomat, 32(16), (2018).
  • Şenyurt, S. and Kılıçoğlu S, On the differential geometric elements of the involute ˜D scroll, Adv. Appl. Clifford Algebras, 25(4)(2015), 977-988, doi:10.1007/s00006-015-0535-z.
There are 11 citations in total.

Details

Primary Language English
Journal Section Volume V Issue II 2020
Authors

Şeyda Kılıçoglu

Publication Date October 31, 2020
Published in Issue Year 2020 Volume: 5 Issue: 2

Cite

APA Kılıçoglu, Ş. (2020). An Examination on the Striction Curves in Terms of Special Ruled Surfaces. Turkish Journal of Science, 5(2), 118-123.
AMA Kılıçoglu Ş. An Examination on the Striction Curves in Terms of Special Ruled Surfaces. TJOS. October 2020;5(2):118-123.
Chicago Kılıçoglu, Şeyda. “An Examination on the Striction Curves in Terms of Special Ruled Surfaces”. Turkish Journal of Science 5, no. 2 (October 2020): 118-23.
EndNote Kılıçoglu Ş (October 1, 2020) An Examination on the Striction Curves in Terms of Special Ruled Surfaces. Turkish Journal of Science 5 2 118–123.
IEEE Ş. Kılıçoglu, “An Examination on the Striction Curves in Terms of Special Ruled Surfaces”, TJOS, vol. 5, no. 2, pp. 118–123, 2020.
ISNAD Kılıçoglu, Şeyda. “An Examination on the Striction Curves in Terms of Special Ruled Surfaces”. Turkish Journal of Science 5/2 (October 2020), 118-123.
JAMA Kılıçoglu Ş. An Examination on the Striction Curves in Terms of Special Ruled Surfaces. TJOS. 2020;5:118–123.
MLA Kılıçoglu, Şeyda. “An Examination on the Striction Curves in Terms of Special Ruled Surfaces”. Turkish Journal of Science, vol. 5, no. 2, 2020, pp. 118-23.
Vancouver Kılıçoglu Ş. An Examination on the Striction Curves in Terms of Special Ruled Surfaces. TJOS. 2020;5(2):118-23.