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

Year 2016, Volume: 2 Issue: 2, 109 - 119, 25.12.2016

Süha Yılmaz Yasin Ünlütürk

Abstract

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

Keywords

A regular plane curve Euclidean plane Bishop frame Smarandache curves

References

  • [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.

Year 2016, Volume: 2 Issue: 2, 109 - 119, 25.12.2016

Süha Yılmaz Yasin Ünlütürk

Abstract

References

  • [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.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Issue
Authors

Süha Yılmaz

Yasin Ünlütürk

Publication Date December 25, 2016
Published in Issue Year 2016 Volume: 2 Issue: 2

Cite

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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