TY  - JOUR
TT  - A NOTE ON SOME CHARACTERIZATIONS OF CURVES DUE TO BISHOP FRAME IN EUCLIDEAN PLANE E2
AU  - Yılmaz, Süha
AU  - Ünlütürk, Yasin
PY  - 2016
DA  - December
JF  - Kirklareli University Journal of Engineering and Science
JO  - KLUJES
PB  - Kirklareli University
WT  - DergiPark
SN  - 2458-7494
SP  - 109
EP  - 119
VL  - 2
IS  - 2
LA  - en
KW  - A regular plane curve
KW  - Euclidean plane
KW  - Bishop frame
KW  - Smarandache curves
N2  - In this paper, we first obtain the differential equation characterizing position vector of a regularcurve 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 somecharacterizations of these special curves due to the Bishop frame in Euclidean plane 2 E .AMS Subject Classification: 53A35, 53A40, 53B25
CR  - [1] A.T. Ali, Special Smarandache curves in the Euclidean space. Int J Math Comb 2:30-36 2010.
CR  - [2] Bishop LR(1975) There is more than one way to frame a curve. Am Math Mon 82:246-251
CR  - [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.
CR  - [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.
CR  - [5] L. Euler, De curvis triangularibus, Acta Acad. Petropol., 3-30, 1778 (1780).
CR  - [6] Fujivara M (1914) On space curves of constant breadth. Tohoku Math J 5:179-184.
CR  - [7] C. G. Gibson, Elementary geometry of differentiable curves. An undergraduate introduction.
Cambridge University Press, Cambridge, 2001.
CR  - [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
CR  - [9] S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turkish J. Math.
28(2), 2004,531-537.
CR  - [10] S. Izumiya, D. Pei, T. Sano, E. Torii, Evolutes of hyperbolic plane curves, Acta Math. Sin.(Engl. Ser.), 20 (2004), 543--550.
CR  - [11] M.K. Karacan, B. Bükçü, Parallel curve (offset) in Euclidean plane, Erciyes Üniversitesi Fen
Bilimleri Enstitüsü Dergisi 24 (1-2) 334- 345 (2008)
CR  - [12] Köse Ö (1984) Some properties of ovals and curves of constant width in a plane. Doğa Turk
J Math (8) 2:119-126
CR  - [13] Köse Ö (1986) On space curves of constant breadth. Doğa Turk J Math (10)1:11--14
CR  - [14] R. Lopez, The theorem of Schur in the Minkowski plane, Jour Geom Phys 61 (2011) 342--
346
CR  - [15] A. Mağden, Ö. Köse, On the curves of constant breadth in space, Turk. J. of Mathematics,
21(3) (1997), 277-284.
CR  - [16] M. Turgut, S. Y lmaz, Smarandache curves in Minkowski space-time, International J. Math.
Combin. 2008; 3,: 51-55.
CR  - [17] Turgut (2009) Smarandache breadth pseudo null curves in Minkowski space-time. Int J
Math Comb 1:46-49.
UR  - https://dergipark.org.tr/en/pub/klujes/article/406918
L1  - https://dergipark.org.tr/en/download/article-file/442560
ER  -