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Curves According to the Successor Frame in Euclidean 3-Space

Year 2018, Volume: 22 Issue: 6, 1868 - 1873, 01.12.2018
https://doi.org/10.16984/saufenbilder.425519

Abstract

In the
present study, the successor formulae of the successor curves defined by
Menninger [1] are given. Then, by defining the successor planes, the geometric
meanings of the successor curvatures are investigated and the relations across
the components of the position vectors of successor curves are found.
Furthermore, in this study, it is proven that lies in the 3rd.type successor
plane,  lies in the 1st type successor
plane and by defining the involute-evolute S-pair, the distance between the
corresponding points of these curves is found.

References

  • Menninger, A. (2014) Characterization of the slant helix as successor curves of the general helix. International Electronic Journal of Geometry, 7(2):84-91.
  • Ali, A.T. (2011) Position vectors of general helices in Euclidean 3-space. Bull. Math. Analy. Appl. 3 (2): 198-205.
  • Bertrand, J. (1850) La theories de courbes a double courbure. J. Math. Pures et Appl. 15: 332-350.
  • Do Carmo, M.P. (1976) Differential geometry of curves and surfaces. Prentice Hall, Englewood Cliffs, New Jersey.
  • Fuchs, D. (2013) Evolutes and involutes of spatial curves. Amer. Math. Monthly, 120(3):217-231.
  • Izumiya, S. & Takeuchi, N. (2002) Generic properties of helices and Bertand curves. J. Geom., 71(1): 97-109.
  • Liu, H. & Wang F., (2008) Mannheim partner curves in 3-space. J. Geom., 88: 120-126.
  • Lucas, P. & Ortega-Yagues, J.A.,(2012) Bertrand curves in the three-dimensional sphere. J. Geom. Phys., 62(9): 1903-1914.
  • Orbay, K. & Kasap, E. (2009) On Mannheim partner curves in . Int. J. Phys. Sci., 4(5): 261-264.
  • Struik, D.J. (1988) Lectures on classical differential geometry. Dover, New-York.
  • Bektaş, Ö. & Yüce, S. (2013) Special involute-evolute partner D-curves in. European Journal of Pure and Applied Mathematics, 6(1):20-29.
  • Bükcü, B. & Karacan, M.K. (2009) The slant helices according to Bishop frame,.World Academy of Science, Engineering and Technology, 59:1039-1042.
  • Yılmaz, S. & Turgut, M. (2010) A new version of Bishop frame and application to spherical images. J. Math. Anal. Appl., 371: 764-776.
Year 2018, Volume: 22 Issue: 6, 1868 - 1873, 01.12.2018
https://doi.org/10.16984/saufenbilder.425519

Abstract

References

  • Menninger, A. (2014) Characterization of the slant helix as successor curves of the general helix. International Electronic Journal of Geometry, 7(2):84-91.
  • Ali, A.T. (2011) Position vectors of general helices in Euclidean 3-space. Bull. Math. Analy. Appl. 3 (2): 198-205.
  • Bertrand, J. (1850) La theories de courbes a double courbure. J. Math. Pures et Appl. 15: 332-350.
  • Do Carmo, M.P. (1976) Differential geometry of curves and surfaces. Prentice Hall, Englewood Cliffs, New Jersey.
  • Fuchs, D. (2013) Evolutes and involutes of spatial curves. Amer. Math. Monthly, 120(3):217-231.
  • Izumiya, S. & Takeuchi, N. (2002) Generic properties of helices and Bertand curves. J. Geom., 71(1): 97-109.
  • Liu, H. & Wang F., (2008) Mannheim partner curves in 3-space. J. Geom., 88: 120-126.
  • Lucas, P. & Ortega-Yagues, J.A.,(2012) Bertrand curves in the three-dimensional sphere. J. Geom. Phys., 62(9): 1903-1914.
  • Orbay, K. & Kasap, E. (2009) On Mannheim partner curves in . Int. J. Phys. Sci., 4(5): 261-264.
  • Struik, D.J. (1988) Lectures on classical differential geometry. Dover, New-York.
  • Bektaş, Ö. & Yüce, S. (2013) Special involute-evolute partner D-curves in. European Journal of Pure and Applied Mathematics, 6(1):20-29.
  • Bükcü, B. & Karacan, M.K. (2009) The slant helices according to Bishop frame,.World Academy of Science, Engineering and Technology, 59:1039-1042.
  • Yılmaz, S. & Turgut, M. (2010) A new version of Bishop frame and application to spherical images. J. Math. Anal. Appl., 371: 764-776.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Melek Masal 0000-0001-6712-7629

Publication Date December 1, 2018
Submission Date May 21, 2018
Acceptance Date September 24, 2018
Published in Issue Year 2018 Volume: 22 Issue: 6

Cite

APA Masal, M. (2018). Curves According to the Successor Frame in Euclidean 3-Space. Sakarya University Journal of Science, 22(6), 1868-1873. https://doi.org/10.16984/saufenbilder.425519
AMA Masal M. Curves According to the Successor Frame in Euclidean 3-Space. SAUJS. December 2018;22(6):1868-1873. doi:10.16984/saufenbilder.425519
Chicago Masal, Melek. “Curves According to the Successor Frame in Euclidean 3-Space”. Sakarya University Journal of Science 22, no. 6 (December 2018): 1868-73. https://doi.org/10.16984/saufenbilder.425519.
EndNote Masal M (December 1, 2018) Curves According to the Successor Frame in Euclidean 3-Space. Sakarya University Journal of Science 22 6 1868–1873.
IEEE M. Masal, “Curves According to the Successor Frame in Euclidean 3-Space”, SAUJS, vol. 22, no. 6, pp. 1868–1873, 2018, doi: 10.16984/saufenbilder.425519.
ISNAD Masal, Melek. “Curves According to the Successor Frame in Euclidean 3-Space”. Sakarya University Journal of Science 22/6 (December 2018), 1868-1873. https://doi.org/10.16984/saufenbilder.425519.
JAMA Masal M. Curves According to the Successor Frame in Euclidean 3-Space. SAUJS. 2018;22:1868–1873.
MLA Masal, Melek. “Curves According to the Successor Frame in Euclidean 3-Space”. Sakarya University Journal of Science, vol. 22, no. 6, 2018, pp. 1868-73, doi:10.16984/saufenbilder.425519.
Vancouver Masal M. Curves According to the Successor Frame in Euclidean 3-Space. SAUJS. 2018;22(6):1868-73.

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