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A NOTE ON SOME CHARACTERIZATIONS OF CURVES DUE TO BISHOP FRAME IN EUCLIDEAN PLANE E2

Yıl 2016, Cilt: 2 Sayı: 2, 109 - 119, 25.12.2016

Süha Yılmaz Yasin Ünlütürk

Öz

In this paper, we first obtain the differential equation characterizing position vector of a regular

curve in Euclidean plane 2 E . Then we study the special curves such as Smarandache curves,

curves of constant breadth due to the Bishop frame in Euclidean plane 2 E . We give some

characterizations of these special curves due to the Bishop frame in Euclidean plane 2 E .

AMS Subject Classification: 53A35, 53A40, 53B25

Anahtar Kelimeler

A regular plane curve Euclidean plane Bishop frame Smarandache curves

Kaynakça

  • [1] A.T. Ali, Special Smarandache curves in the Euclidean space. Int J Math Comb 2:30-36 2010.
  • [2] Bishop LR(1975) There is more than one way to frame a curve. Am Math Mon 82:246-251
  • [3] M. Çetin, Y. Tuncer Y and M.K. Karacan, Smarandache curves according to Bishop frame in Euclidean 3-space, Gen. Math. Notes, 2014; 20: 50-56.
  • [4] B.Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly 110 (2003), 147-152.
  • [5] L. Euler, De curvis triangularibus, Acta Acad. Petropol., 3-30, 1778 (1780).
  • [6] Fujivara M (1914) On space curves of constant breadth. Tohoku Math J 5:179-184.
  • [7] C. G. Gibson, Elementary geometry of differentiable curves. An undergraduate introduction. Cambridge University Press, Cambridge, 2001.
  • [8] A. Gray, E. Abbena, S. Salamon, Modern differential geometry of curves and surfaces with Mathematica Chapman and Hall/CRC, Boca Raton, FL, (2006). 1
  • [9] S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turkish J. Math. 28(2), 2004,531-537.
  • [10] S. Izumiya, D. Pei, T. Sano, E. Torii, Evolutes of hyperbolic plane curves, Acta Math. Sin.(Engl. Ser.), 20 (2004), 543--550.
  • [11] M.K. Karacan, B. Bükçü, Parallel curve (offset) in Euclidean plane, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24 (1-2) 334- 345 (2008)
  • [12] Köse Ö (1984) Some properties of ovals and curves of constant width in a plane. Doğa Turk J Math (8) 2:119-126
  • [13] Köse Ö (1986) On space curves of constant breadth. Doğa Turk J Math (10)1:11--14
  • [14] R. Lopez, The theorem of Schur in the Minkowski plane, Jour Geom Phys 61 (2011) 342-- 346
  • [15] A. Mağden, Ö. Köse, On the curves of constant breadth in space, Turk. J. of Mathematics, 21(3) (1997), 277-284.
  • [16] M. Turgut, S. Y lmaz, Smarandache curves in Minkowski space-time, International J. Math. Combin. 2008; 3,: 51-55.
  • [17] Turgut (2009) Smarandache breadth pseudo null curves in Minkowski space-time. Int J Math Comb 1:46-49.

Yıl 2016, Cilt: 2 Sayı: 2, 109 - 119, 25.12.2016

Süha Yılmaz Yasin Ünlütürk

Öz

Kaynakça

  • [1] A.T. Ali, Special Smarandache curves in the Euclidean space. Int J Math Comb 2:30-36 2010.
  • [2] Bishop LR(1975) There is more than one way to frame a curve. Am Math Mon 82:246-251
  • [3] M. Çetin, Y. Tuncer Y and M.K. Karacan, Smarandache curves according to Bishop frame in Euclidean 3-space, Gen. Math. Notes, 2014; 20: 50-56.
  • [4] B.Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly 110 (2003), 147-152.
  • [5] L. Euler, De curvis triangularibus, Acta Acad. Petropol., 3-30, 1778 (1780).
  • [6] Fujivara M (1914) On space curves of constant breadth. Tohoku Math J 5:179-184.
  • [7] C. G. Gibson, Elementary geometry of differentiable curves. An undergraduate introduction. Cambridge University Press, Cambridge, 2001.
  • [8] A. Gray, E. Abbena, S. Salamon, Modern differential geometry of curves and surfaces with Mathematica Chapman and Hall/CRC, Boca Raton, FL, (2006). 1
  • [9] S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turkish J. Math. 28(2), 2004,531-537.
  • [10] S. Izumiya, D. Pei, T. Sano, E. Torii, Evolutes of hyperbolic plane curves, Acta Math. Sin.(Engl. Ser.), 20 (2004), 543--550.
  • [11] M.K. Karacan, B. Bükçü, Parallel curve (offset) in Euclidean plane, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24 (1-2) 334- 345 (2008)
  • [12] Köse Ö (1984) Some properties of ovals and curves of constant width in a plane. Doğa Turk J Math (8) 2:119-126
  • [13] Köse Ö (1986) On space curves of constant breadth. Doğa Turk J Math (10)1:11--14
  • [14] R. Lopez, The theorem of Schur in the Minkowski plane, Jour Geom Phys 61 (2011) 342-- 346
  • [15] A. Mağden, Ö. Köse, On the curves of constant breadth in space, Turk. J. of Mathematics, 21(3) (1997), 277-284.
  • [16] M. Turgut, S. Y lmaz, Smarandache curves in Minkowski space-time, International J. Math. Combin. 2008; 3,: 51-55.
  • [17] Turgut (2009) Smarandache breadth pseudo null curves in Minkowski space-time. Int J Math Comb 1:46-49.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Sayı
Yazarlar

Süha Yılmaz

Yasin Ünlütürk

Yayımlanma Tarihi 25 Aralık 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 2 Sayı: 2

Kaynak Göster

APA Yılmaz, S., & Ünlütürk, Y. (2016). A NOTE ON SOME CHARACTERIZATIONS OF CURVES DUE TO BISHOP FRAME IN EUCLIDEAN PLANE E2. Kırklareli Üniversitesi Mühendislik Ve Fen Bilimleri Dergisi, 2(2), 109-119.
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