Araştırma Makalesi
BibTex RIS Kaynak Göster

ON CURVES OF CONSTANT WIDTH DUE TO THE BISHOP FRAME OF TYPE-2 IN DUAL EUCLIDEAN SPACE D^3

Yıl 2016, Cilt: 2 Sayı: 1, 13 - 21, 30.06.2016

Yasin Ünlütürk

Öz

In this work, we study dual constant width curves due to the Bishop frame of type-2 in

dual space 3 D . We obtain a differential equation which characterizes these curves in 𝐷^3. For

special solutions of this differential equation system, we obtain some results in 𝐷^3.

Anahtar Kelimeler

Dual curves dual constant width curves dual Bishop frame of type-2 dual Euclidean space

Kaynakça

  • [1] Bishop, L.R., There is More Than One Way to Frame a Curve, Amer. Math. Monthly 82, 246-251, 1975.
  • [2] Blaschke, W., Konvexe Bereiche Gegebener Konstanter Breite und Kleinsten Inhalts. Math. Ann. 76, 504-513, 1915.
  • [3] Euler, L., De Curvis Trangularibus, Acta Acad Petropol, 1870.
  • [4] Fujivara, M., On Space Curves of Constant Breadth, Tohoku Math. J. 5, 179-184, 1963.
  • [5] Köse, Ö., On Space Curves of Constant Breadth, Doğa Turk. J. Math. 10, 1, 11-14, 1986.
  • [6] Reuleaux, F., The Kinematics of Machinery, Dover Publications, New York, 1963.
  • [7] Veldkamp, G.R., On The Use of Dual Numbers, Vectors and Matrices in Instantaneous Spatial Kinematics, Mech. Math. Theory, 11, 141-156, 1976.
  • [8] Yılmaz, S., Turgut, M., A New version of Bishop Frame and Application to Spherical Images , Journal of Mathematical Analysis and Applications, 371, 764-776, 2010.
  • [9] Yılmaz, S., Savcı, Ü.Z., Dual Curves of Constant Breadth According to Bishop Frame in Dual Euclidean Space, Mathematical Sciences Letters, 1, 1-4 , 2016.
  • [10] Yılmaz, S., Savcı, Ü.Z., and Ünlütürk, Y., On Dual Spacelike Curves Of Constant Breadth In Dual Lorentzian Space D13, New Trends In Mathematical Sciences, 3, 4, 164– 170, 2015.
  • [11] Yılmaz, S., Savcı, Ü.Z., and Ünlütürk, Y., Spacelike Curves of Constant Breadth According to Bishop Frame in Minkowski 3-space, International J. Math. Combin., 4, 4, 1–6, 2014.
  • [12] Mağden, A., Yılmaz, S., On The Curves Of Constant Breadth In Four Dimensional Galilean Space, International Mathematical Forum, 9, 25, 229–1236, 2014.
  • [13] Yılmaz, S., and Turgut, M., Partially Null Curves of Constant Breadth in Semi- Riemannian Space, Modern Applied Science, 3, 3, 60–63, 2009.
  • [14] Yılmaz, S., Savcı, Ü.Z., and Turgut, M., Characterizations of curves of constant breadth in Galilean 3-space G3, Journal of Advanced Research in Pure Mathematics, 6, 1, 19–24, 2014.
  • [15] Yılmaz, S., and Turgut, M., On the Time-like Curves of Constant Breadth in Minkowski 3-Space,” International Journal of Mathematical Combinatorics, 3, 34–39, 2008.

Yıl 2016, Cilt: 2 Sayı: 1, 13 - 21, 30.06.2016

Yasin Ünlütürk

Öz

Kaynakça

  • [1] Bishop, L.R., There is More Than One Way to Frame a Curve, Amer. Math. Monthly 82, 246-251, 1975.
  • [2] Blaschke, W., Konvexe Bereiche Gegebener Konstanter Breite und Kleinsten Inhalts. Math. Ann. 76, 504-513, 1915.
  • [3] Euler, L., De Curvis Trangularibus, Acta Acad Petropol, 1870.
  • [4] Fujivara, M., On Space Curves of Constant Breadth, Tohoku Math. J. 5, 179-184, 1963.
  • [5] Köse, Ö., On Space Curves of Constant Breadth, Doğa Turk. J. Math. 10, 1, 11-14, 1986.
  • [6] Reuleaux, F., The Kinematics of Machinery, Dover Publications, New York, 1963.
  • [7] Veldkamp, G.R., On The Use of Dual Numbers, Vectors and Matrices in Instantaneous Spatial Kinematics, Mech. Math. Theory, 11, 141-156, 1976.
  • [8] Yılmaz, S., Turgut, M., A New version of Bishop Frame and Application to Spherical Images , Journal of Mathematical Analysis and Applications, 371, 764-776, 2010.
  • [9] Yılmaz, S., Savcı, Ü.Z., Dual Curves of Constant Breadth According to Bishop Frame in Dual Euclidean Space, Mathematical Sciences Letters, 1, 1-4 , 2016.
  • [10] Yılmaz, S., Savcı, Ü.Z., and Ünlütürk, Y., On Dual Spacelike Curves Of Constant Breadth In Dual Lorentzian Space D13, New Trends In Mathematical Sciences, 3, 4, 164– 170, 2015.
  • [11] Yılmaz, S., Savcı, Ü.Z., and Ünlütürk, Y., Spacelike Curves of Constant Breadth According to Bishop Frame in Minkowski 3-space, International J. Math. Combin., 4, 4, 1–6, 2014.
  • [12] Mağden, A., Yılmaz, S., On The Curves Of Constant Breadth In Four Dimensional Galilean Space, International Mathematical Forum, 9, 25, 229–1236, 2014.
  • [13] Yılmaz, S., and Turgut, M., Partially Null Curves of Constant Breadth in Semi- Riemannian Space, Modern Applied Science, 3, 3, 60–63, 2009.
  • [14] Yılmaz, S., Savcı, Ü.Z., and Turgut, M., Characterizations of curves of constant breadth in Galilean 3-space G3, Journal of Advanced Research in Pure Mathematics, 6, 1, 19–24, 2014.
  • [15] Yılmaz, S., and Turgut, M., On the Time-like Curves of Constant Breadth in Minkowski 3-Space,” International Journal of Mathematical Combinatorics, 3, 34–39, 2008.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Sayı
Yazarlar

Yasin Ünlütürk

Yayımlanma Tarihi 30 Haziran 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 2 Sayı: 1

Kaynak Göster

APA Ünlütürk, Y. (2016). ON CURVES OF CONSTANT WIDTH DUE TO THE BISHOP FRAME OF TYPE-2 IN DUAL EUCLIDEAN SPACE D^3. Kırklareli Üniversitesi Mühendislik Ve Fen Bilimleri Dergisi, 2(1), 13-21.
 Kapak Resmi İndir