Communications in Advanced Mathematical Sciences
Research Article
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Year 2020, Volume: 3 Issue: 1, 1 - 8, 25.03.2020

Süleyman ŞENYURT Yasin ALTUN

https://doi.org/10.33434/cams.594690
Cited By: 3

Abstract

References

  • [1] A.T. Ali, Special Smarandache Curves in the Euclidian Space, International J.Math. Combin., 2, (2010), 30-36.
  • [2] A. Çalışkan, S. Şenyurt, Smarandache Curves In Terms of Sabban Frame of Spherical Indicatrix Curves, Gen. Math. Notes, 31(2), (2015), 1-15.
  • [3] A. Sabuncuoğlu, Differential Geometry, Nobel Publications, 2006.
  • [4] J. Koenderink, Solid Shape, MIT Press, Cambridge, MA, 1990.
  • [5] K. Taşköprü, M. Tosun, Smarandache Curves on S2, Bol. Soc. Paran. Mat. 32(1), (2014), 51-59.
  • [6] M. Turgut, S. Yılmaz, Smarandache Curves in Minkowski space-time, International J.Math. Combin., 3, (2008), 51-55.
  • [7] S. Şenyurt, C. Cevahir, Y. Altun, On Spatial Quaternionic Involute Curve A New View, Adv. Appl. Clifford Algebras, 27(2), (2017), 1815-1824.
  • [8] S. Şenyurt, C. Cevahir, Y. Altun, H. Kocayi˘git, On the Sabban frame belonging to involute-evolute curves, Thermal Science, 23, (2019), 413-425.
  • [9] K. E. Özen, M. Tosun, M. Akyiğit, Siacci’s theorem according to Darboux frame, Analele Universitatii Ovidius Constanta-Seria Matematica, 25(3), (2017), 155–165. DOI:10.1515/auom-2017-0042.
  • [10] K. E. Özen, F. S. Dündar, M. Tosun, An alternative approach to jerk in motion along a space curve with applications, Journal of Theoretical and Applied Mechanics, 57(2), (2019), 435–444. DOI:10.15632/jtam-pl/104595.
  • [11] K. E. Özen, M. Güner, M. Tosun, A note on the acceleration and jerk in motion along a space curve, Analele Universitatii Ovidius Constanta-Seria Matematica, 28(1), (2020), 151-164. DOI:10.2478/auom-2020-0011.
  • [12] W. Fenchel, On The Differential Geometry of Closed Space Curves, Bulletin of the American Mathematical Society, 57, (1951), 44-54.

Smarandache Curves of the Evolute Curve According to Sabban Frame

Year 2020, Volume: 3 Issue: 1, 1 - 8, 25.03.2020

Süleyman ŞENYURT Yasin ALTUN

https://doi.org/10.33434/cams.594690
Cited By: 3

Abstract

The aim of this paper is to define Smarandache curves according to the Sabban frame belonging to the unit Darboux vector of spherical indicatrix curve of the evolute curve. Also, we calculate the geodesic curvatures of these curves. Finally, the results are expressed depending on the involute curve.

Keywords

Darboux vector, Involute curve, Evolute curve, Geodesic curvature, Sabban frame, Smarandache curves

References

  • [1] A.T. Ali, Special Smarandache Curves in the Euclidian Space, International J.Math. Combin., 2, (2010), 30-36.
  • [2] A. Çalışkan, S. Şenyurt, Smarandache Curves In Terms of Sabban Frame of Spherical Indicatrix Curves, Gen. Math. Notes, 31(2), (2015), 1-15.
  • [3] A. Sabuncuoğlu, Differential Geometry, Nobel Publications, 2006.
  • [4] J. Koenderink, Solid Shape, MIT Press, Cambridge, MA, 1990.
  • [5] K. Taşköprü, M. Tosun, Smarandache Curves on S2, Bol. Soc. Paran. Mat. 32(1), (2014), 51-59.
  • [6] M. Turgut, S. Yılmaz, Smarandache Curves in Minkowski space-time, International J.Math. Combin., 3, (2008), 51-55.
  • [7] S. Şenyurt, C. Cevahir, Y. Altun, On Spatial Quaternionic Involute Curve A New View, Adv. Appl. Clifford Algebras, 27(2), (2017), 1815-1824.
  • [8] S. Şenyurt, C. Cevahir, Y. Altun, H. Kocayi˘git, On the Sabban frame belonging to involute-evolute curves, Thermal Science, 23, (2019), 413-425.
  • [9] K. E. Özen, M. Tosun, M. Akyiğit, Siacci’s theorem according to Darboux frame, Analele Universitatii Ovidius Constanta-Seria Matematica, 25(3), (2017), 155–165. DOI:10.1515/auom-2017-0042.
  • [10] K. E. Özen, F. S. Dündar, M. Tosun, An alternative approach to jerk in motion along a space curve with applications, Journal of Theoretical and Applied Mechanics, 57(2), (2019), 435–444. DOI:10.15632/jtam-pl/104595.
  • [11] K. E. Özen, M. Güner, M. Tosun, A note on the acceleration and jerk in motion along a space curve, Analele Universitatii Ovidius Constanta-Seria Matematica, 28(1), (2020), 151-164. DOI:10.2478/auom-2020-0011.
  • [12] W. Fenchel, On The Differential Geometry of Closed Space Curves, Bulletin of the American Mathematical Society, 57, (1951), 44-54.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Süleyman ŞENYURT
ORDU UNIVERSITY
0000-0003-1097-5541
Türkiye

Yasin ALTUN This is me
Emniyet Teşkilatı
0000-0002-6977-4958
Türkiye

Publication Date March 25, 2020
Submission Date July 21, 2019
Acceptance Date January 23, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

Bibtex @research article { cams594690, journal = {Communications in Advanced Mathematical Sciences}, issn = {2651-4001}, address = {}, publisher = {Emrah Evren KARA}, year = {2020}, volume = {3}, number = {1}, pages = {1 - 8}, doi = {10.33434/cams.594690}, title = {Smarandache Curves of the Evolute Curve According to Sabban Frame}, key = {cite}, author = {Şenyurt, Süleyman and Altun, Yasin} }
APA Şenyurt, S. & Altun, Y. (2020). Smarandache Curves of the Evolute Curve According to Sabban Frame . Communications in Advanced Mathematical Sciences , 3 (1) , 1-8 . DOI: 10.33434/cams.594690
MLA Şenyurt, S. , Altun, Y. "Smarandache Curves of the Evolute Curve According to Sabban Frame" . Communications in Advanced Mathematical Sciences 3 (2020 ): 1-8 <https://dergipark.org.tr/en/pub/cams/issue/53344/594690>
Chicago Şenyurt, S. , Altun, Y. "Smarandache Curves of the Evolute Curve According to Sabban Frame". Communications in Advanced Mathematical Sciences 3 (2020 ): 1-8
RIS TY - JOUR T1 - Smarandache Curves of the Evolute Curve According to Sabban Frame AU - SüleymanŞenyurt, YasinAltun Y1 - 2020 PY - 2020 N1 - doi: 10.33434/cams.594690 DO - 10.33434/cams.594690 T2 - Communications in Advanced Mathematical Sciences JF - Journal JO - JOR SP - 1 EP - 8 VL - 3 IS - 1 SN - 2651-4001- M3 - doi: 10.33434/cams.594690 UR - https://doi.org/10.33434/cams.594690 Y2 - 2020 ER -
EndNote %0 Communications in Advanced Mathematical Sciences Smarandache Curves of the Evolute Curve According to Sabban Frame %A Süleyman Şenyurt , Yasin Altun %T Smarandache Curves of the Evolute Curve According to Sabban Frame %D 2020 %J Communications in Advanced Mathematical Sciences %P 2651-4001- %V 3 %N 1 %R doi: 10.33434/cams.594690 %U 10.33434/cams.594690
ISNAD Şenyurt, Süleyman , Altun, Yasin . "Smarandache Curves of the Evolute Curve According to Sabban Frame". Communications in Advanced Mathematical Sciences 3 / 1 (March 2020): 1-8 . https://doi.org/10.33434/cams.594690
AMA Şenyurt S. , Altun Y. Smarandache Curves of the Evolute Curve According to Sabban Frame. Communications in Advanced Mathematical Sciences. 2020; 3(1): 1-8.
Vancouver Şenyurt S. , Altun Y. Smarandache Curves of the Evolute Curve According to Sabban Frame. Communications in Advanced Mathematical Sciences. 2020; 3(1): 1-8.
IEEE S. Şenyurt and Y. Altun , "Smarandache Curves of the Evolute Curve According to Sabban Frame", Communications in Advanced Mathematical Sciences, vol. 3, no. 1, pp. 1-8, Mar. 2020, doi:10.33434/cams.594690

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