TY - JOUR TT - A study on the characterizations of non-null curves according to the Bishop frame of type-2 in Minkowski 3-space AU - Yılmaz, Süha AU - Ünlütürk, Yasin AU - Mağden, Abdullah PY - 2016 DA - August Y2 - 2016 DO - 10.16984/saufenbilder.50911 JF - Sakarya University Journal of Science JO - SAUJS PB - Sakarya University WT - DergiPark SN - 2147-835X SP - 325 EP - 335 VL - 20 IS - 2 KW - spacelike eğri KW - timelike eğri KW - konum vektörü KW - bishop düzlemleri KW - 2. tip Bishop çatısı N2 - In this work, we study classical differential geometry of non-null curves according to the new version of Bishop frame in which we call it along the work as “the Bishop frame of type-2”. First, we investigate position vector of a regular non-null curve by obtaining a system of ordinary differential equations. The solution of the system gives the components of the position vector with respect to the Bishop frame of type-2 in . Moreover, we define the first, second and third order Bishop planes according to this new frame, and also, regardig to these planes, we characterize position vectors in . CR - A.T. Ali, M.Turgut, “Position vector of a time-like slant helix in Minkowski 3-space”, J Math Anal Appl, vol. 365, no. 1, pp. 559-569, 2010. CR - L. R. Bishop, There is more than one way to frame a curve, Amer Math Monthly vol. 82, pp.246-251, 1975. CR - B. Y. Chen, “When does the position vector of a space curve always lie in its rectifying plane?”, Amer Math Monthly, vol. 110, pp. 147-152, 2003. CR - B. Divjak, “Curves in pseudo-Galilean geometry”, Annales Univ. Sci. Bud, vol. 41, pp. 117-128, 1998. CR - K. İlarslan, Ö. Boyacıoğlu, “Position vectors of a time-like and a null helix in Minkowski 3-space”, Chaos Solitons Fractals, vol.38, pp. 1383—1389, 2008. CR - R. Lopez, “Differential geometry of curves and surfaces in Lorentz-Minkowski space”, Int. Elec. Journ. Geom. vol. 3, no. 2, pp. 67-101, 2010. CR - B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983. CR - E. Özyılmaz, “Classical differential geometry of curves according to type-2 Bishop trihedra”, Math.Comput. Appl., vol. 16, no.4, pp. 858-867, 2011. CR - M. Turgut, “On the invariants of time-like dual curves”, Hacettepe Jour. Math. Stat., vol. 37, no. 2, pp. 129-133, 2008. CR - M. Turgut, S. Yılmaz, “Contributions to classical differential geometry of the curves in E^3”, Sci. Magna, vol. 4, pp. 5-9, 2008. CR - Y. Ünlütürk, S. Yılmaz, “A new version of Bishop frame and its application to Smarandache curves of a spacelike curve in Minkowski 3-space”, to appear. CR - S. Yılmaz, M. Turgut, “A new version of Bishop frame and an application to spherical images”, J. Math. Anal. Appl., v. 371, pp. 764-776, 2010. CR - S. Yılmaz, “Bishop spherical images of a spacelike curve in Minkowski 3-space”, Int. Jour. Phys. Scie. vol. 5, no. 6, pp. 898-905, 2010. CR - S. Yılmaz, “Position vectors of some special space-like curves according to Bishop frame in Minkowski space E_1^3”, Sci. Magna., vol. 5, no. 1, pp. 58-50, 2009. CR - S. Yılmaz, E. Özyılmaz, M. Turgut, Ş. Nizamoğlu, “Position vector of a partially null curve derived from a vector differential equation, Int. Sch. Scie. Res. & Innov., vol. 3, no. 11, pp. 846-848, 2009. CR - S. Yılmaz , Ü.Z. Savcı, A. Mağden, “Position vector of some special curves in Galilean 3-spaces G_3”, Glo. Jour. Adv. Res. Class. Mod. Geom., vol. 3, no. 1, pp. 7-11, 2014. UR - https://doi.org/10.16984/saufenbilder.50911 L1 - https://dergipark.org.tr/en/download/article-file/227624 ER -