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Öğe Directional del-derivative and Curves on n-dimensional Time Scales(Springer, 2009) Aktan, Nesip; Sarıkaya, Mehmet Zeki; İlarslan, Kazim; Yıldırım, HüseyinThe general ideal in this paper is to study a differential calculus for multivariable functions, directional del-derivative and curves of parametric equations on n-dimensional time scales.Öğe The first kind and the second kind osculating curves in Minkowski space-time(Publ House Bulgarian Acad Sci, 2009) İlarslan, Kazim; Nesovic, EmilijaIn this paper we define the first kind and the second kind osculating curve in Minkowski space-time E-1(4). We restrict our investigation of osculating curves in E-1(4) to spacelike curves whose Frenet frame contains only non-null vector fields, as well as to timelike curves and characterize such curves in terms of their curvature functions. Moreover, we obtain the explicit equations of such osculating curves with constant curvatures.Öğe Position vectors of a spacelike W-curve in minkowski space E1 3(Korean Mathematical Soc, 2007) İlarslan, Kazim; Boyacioglu, ÖzgürIn this paper, we study the position vectors of a spacelike W-curve (or a helix), i.e., curve with constant curvatures, with spacelike, timelike and null principal normal in the Minkowski 3-space E-1(3). We give some chracterizations for spacelike W- curves whose image lies on the pseudohyperbolical space H-0(2) and Lorentzian sphere S-1(2) by using the positions vectors of the curve.Öğe Semi-parallel and harmonic surfaces in semi-euclidean 4-space with index 2(University of Nis, 2019) Yildirim, Mehmet; İlarslan, KazimThe present paper mainly deals with construction and investigation further properties of semi-parallel and harmonic surfaces. The first part of the study shall be devoted to investigate and present necessary and sufficient conditions of being semi-parallel surfaces by considering semi-parallelity condition R(X, Y).h = 0. In the light of the condition, the fact of a part of semi-parallel surfaces can be created by translation surfaces is captured. As a last result, we present that M must be a translation surface in the case of it is a harmonic surface. © 2019, University of Nis. All rights reserved.