Araştırma Makalesi
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Curves According to the Successor Frame in Euclidean 3-Space

Yıl 2018, Cilt: 22 Sayı: 6, 1868 - 1873, 01.12.2018

Melek Masal

https://doi.org/10.16984/saufenbilder.425519
Cited By: 2

Öz

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.

Anahtar Kelimeler

Successor frame Successor curves Slant helix Involute-evolute curves

Kaynakça

  • 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.

Yıl 2018, Cilt: 22 Sayı: 6, 1868 - 1873, 01.12.2018

Melek Masal

https://doi.org/10.16984/saufenbilder.425519
Cited By: 2

Öz

Kaynakça

  • 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.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Melek Masal 0000-0001-6712-7629

Yayımlanma Tarihi 1 Aralık 2018
Gönderilme Tarihi 21 Mayıs 2018
Kabul Tarihi 24 Eylül 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 22 Sayı: 6

Kaynak Göster

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. Aralık 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, sy. 6 (Aralık 2018): 1868-73. https://doi.org/10.16984/saufenbilder.425519.
EndNote Masal M (01 Aralık 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, c. 22, sy. 6, ss. 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 (Aralık 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, c. 22, sy. 6, 2018, ss. 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.

Cited By

Associated curves from a different point of view in $E^3$
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
https://doi.org/10.31801/cfsuasmas.1026359
Spinor Equations of Successor Curves
Universal Journal of Mathematics and Applications
https://doi.org/10.32323/ujma.1070029
 Kapak Resmi İndir

30930  This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.