Sareh MEHDIZADEH GILANI, Yusuf YAYLI, Nemat ABAZARI

Characterizations of dual curves and dual focal curves in dual Lorentzian space D3 1

In this paper, we have introduced dual Lorentzian connection, bracket and curvature tensor on dual Lorentzian space D 3 1. We have studied a dual curve in different situations in dual Lorentzian space D 3 1 and have found Bishop Darboux vector and some relations according to this vector field, Bishop frame and focal curve of the present dual curve. It has been shown that Bishop Darboux vector has a similar amount in three different cases of a dual curve and the first dual focal curvature of the aforementioned curve is constant function.

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[1] Bishop RL. There is more than one way to frame a curve. The American Mathematical Monthly 1975; 82 (3): 246-251.
[2] Bukcu B, Karacan MK. Bishop frame of the spacelike curve with a spacelike principal normal in Minkowski 3-space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2008; 57 (1): 13-22.
[3] Carroll D, Köse E, Sterling I. Improving Frenet’s frame using Bishop’s frame. Journal of Mathematics Research 2013; 5 (4): 97-106.
[4] Kandasamy WBV, Smarandache F. Dual Numbers. Ohio, USA: Zip Publishing, 2012.
[5] Kocayigit H, Bukcu B, Pektas I. Characterizations of spacelike curves according to Bishop Darboux vector in Minkowski 3-space E 3 1 . Communication in Mathematical Modeling and Applications 2016; 2: 1-7.
[6] Korpinar T, Turhan E. Dual spacelike elastic biharmonic curves with timelike principal normal according to dual bishop frames. International Journal of Mathematical Combinatorics 2011; 4: 46-53.
[7] Korpinar T, Turhan E. On characterization of dual Focal curves of spacelike biharmonic curves with timelike binormal in the dual Lorentzian D 3 1 . Studia Universitatis Babes-Bolyai Mathematica 2012; 57 (3): 421- 426.
[8] Kuhnel W. Differential Geometry. Providence, RI, USA: American Mathematical Society, 2002.
[9] Singer DA. Lectures on elastic curves and rods . AIP Conference Proceedings 2008; 1002 (1): 3-32.