POSITION VECTOR OF A DEVELOPABLE h-SLANT RULED SURFACE

Yıl 2017, Cilt: 7 Sayı: 2, 1 - 10, 01.12.2017

O. Kaya M. Önder

Öz

In physics and geometry, the determination of position vector of a moving point is an important problem, since the trajectory of that point is a curve or a surface which are important in physics, geometry, and applied sciences. By considering this importance, in this paper, we give a new characterization for a special ruled surface called h-slant ruled surface in the Euclidean 3-space E3. Later, using the obtained result, we study the position vector of a developable h-slant ruled surface in E3. We obtain the natural representations for the striction curve and ruling of an h-slant ruled surface. Then, we give general parameterization of a developable h-slant ruled surface. Finally, we introduce some examples of obtained results.

Anahtar Kelimeler

position vector, slant ruled surface, developable ruled surface.

Kaynakça

• [1] Ali,A.T., (2010), Position vectors of spacelike general helices in Minkowski 3-space, Nonl. Anal. Theory Meth. Appl., 73, pp.1118-1126.
• [2] Ali,A.T. and Turgut,M., (2013), Position vectors of a timelike general helices in Minkowski 3-space, Glob. J. Adv. Res. Class. Mod. Geom., 2(1), pp.1-10.
• [3] Ali,A.T. and Turgut,M., (2010), Position vector of a timelike slant helix in Minkowski 3-space, J. Math. Anal. Appl., 365, pp.559-569.
• [4] Ali,A.T., (2012), Position vectors of slant helices in Euclidean Space E 3 , J of Egyptian Math Soc., 20 (1), pp.1-6.
• [5] Ali,A.T., (2011), Position Vectors of General Helices in Euclidean 3-space, Bulletin of Math. Analysis and App., 3 (2), pp.198-205.
• [6] Barros,M., (1997) General helices and a theorem of Lancret. Proc Amer Math Soc, 125(5), pp.1503- 1509.
• [7] Chen,B.Y., (2003), When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Mounthly, 110 (2), pp.147-152.
• [8] Izumiya,S and Takeuchi,N., (2004), New special curves and developable surfaces, Turk J Math., 28, pp.153-163.
• [9] ˙Ilarslan,K. and Boyacıo˘glu,O., (2007), Position vectors of a spacelike W-curve in Minkowski Space E 3 1 , Bull. Korean Math. Soc., 44, pp.429-438.
• [10] ˙Ilarslan,K. and Boyacıo˘glu,O., (2008), Position vectors of a timelike and a null helix in Minkowski 3-space, Chaos, Solitons and Fractals, 38, pp.1383-1389.
• [11] Karger,A. and Novak,J., (1978), Space Kinematics and Lie Groups. Prague, Czechoslovakia: STNL Publishers of Technical Lit.
• [12] Kaya,O. and Onder,M., Characterizations of Slant Ruled Surfaces in the Euclidean 3-space, Caspian ¨ Journal of Mathematical Sciences, (in press).
• [13] Kula,L. and Yaylı,Y., (2005), On slant helix and its spherical indicatrix. Appl. Math. Comp., 169, pp.600-607.
• [14] Kula,L., Ekmek¸ci,N., Yaylı,Y., and ˙Ilarslan,K., (2009), Characterizations of Slant Helices in Euclidean 3-Space, Turk J Math., 33, pp.1-13.
• [15] Onder,M. and Kaya,O., (2015), Darboux Slant Ruled Surfaces, Azerbaijan Journal of Mathematics, ¨ 5 (1), pp.64-72.
• [16] Onder,M., (2013), Slant Ruled Surfaces in the Euclidean 3-space ¨ E 3 , arXiv:1311.0627v1 [math.DG].
• [17] Onder,M., Kazaz,M., Kocayi˘git,H., and Kılı¸c, O.,(2008), ¨ B2-slant helix in Euclidean 4-space E 4 , Int J Contemp Math Sci., 3 (29-32), pp.1433-1440.
• [18] Onder,M., Zıplar,E., and Kaya,O., (2014), Eikonal slant helices and Eikonal Darboux helices in 3- ¨ dimensional Riemannian Manifold, International Journal of Geometric Methods in Modern Physics, Vol. 11, 1450045 (10 pages).