Position vectors of curves with recpect to Darboux frame in the Galilean space G³
In this paper, we investigate the position vector of a curve on the surface in the Galilean 3-space G³. Firstly, the position vector of a curve with respect to the Darboux frame is determined. Secondly, we obtain the standard representation of the position vector of the curve with respect to Darboux frame in terms of the geodesic, normal curvature and geodesic torsion. As a result of this, we define the position vectors of geodesic, asymptotic and normal line along with some special curves with respect to Darboux frame. Finally, we elaborate on some examples and provide their graphs.
Keywords:
Position vector, Darboux frame geodesic, Galilean 3-space,
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- Kreyszig, E., Differential Geometry, Dover Publications, Reprint, New York, 1991.
- McCleary, J., Geoemetry From a Differentiable Viewpoint, Cambridge University Press, 1994.
- Ali, A.T., Position vectors of curves in the Galilean space G³, Matematicki Vesnik, 64(3) (2012), 200--210.
- Ali, A.T., Position vectors of spacelike general helices in Minkowski 3-space, Nonlin. Anal. Theory Meth. Appl. 73(2010), 1118--1126.
- Ali, A.T., Position vectors of slant helices in Euclidean 3-space, Journal of the Egyptian Mathematical Society, 20(1) (2012), 1--6.
- Izumiya, S. and Takeuchi, N., New special curves and developable surfaces, Turk. J. Math. 28(2004), 531--537.
- Molnar, E., The projective interpretation of the eight 3-dimensional homogeneous geometries, Beitr. Algebra Geom. 38(1997), 261--288
- Pavković, B.J. and Kamenarović, I., The equiform differential geometry of curves in the Galilean space, Glasnik Matematikci. 22(42) (1987), 449--457.
- Pavković, B.J. , The general solution of the Frenet system of differential equations for curves in the Galilean space G³, Rad HAZU Math. 450 (1990), 123--128.
- Şahin, T., Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean space, Acta Math Sci. 33B(3) (2013) 701--711.
- Roschel, O., Die Geometrie des Galileischen Raumes, Habilitation Schrift, Leoben 1984.
- Yaglom, I. M. , A simple non-Euclidean geometry and its physical basis, Springer-Verlag, Nw York, 1979.
- Monterde, J., Salkowski curves revisted: A family of curves with constant curvature and non-constant torsion, Comput. Aided Geomet. Design. 26 (2009), 271--278.
- Salkowski, E., Zur transformation von raumkurven, Math. Ann. 66 (1909), 517- 557.
- Şahin, T. and Okur, M., Special Smarandache curves with respect to Darboux frame in Galilean 3-Space, Int. J. Adv. Appl. Math. and Mech. 5(3)(2018), 15--26 (ISSN: 2347-2529).
- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi
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