Yazar "İlarslan, Kazim" seçeneğine göre listele

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    Directional del-derivative and Curves on n-dimensional Time Scales
    (Springer, 2009) Aktan, Nesip; Sarıkaya, Mehmet Zeki; İlarslan, Kazim; Yıldırım, Hüseyin
    The 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.
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    The first kind and the second kind osculating curves in Minkowski space-time
    (Publ House Bulgarian Acad Sci, 2009) İlarslan, Kazim; Nesovic, Emilija
    In 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.
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    Position vectors of a spacelike W-curve in minkowski space E1 3
    (Korean Mathematical Soc, 2007) İlarslan, Kazim; Boyacioglu, Özgür
    In 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.
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    Semi-parallel and harmonic surfaces in semi-euclidean 4-space with index 2
    (University of Nis, 2019) Yildirim, Mehmet; İlarslan, Kazim
    The 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.
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    Space Curves Related by a Transformation of Combescure
    (Taylor & Francis Ltd, 2021) Çamcı, Çetin; Uçum, Ali; İlarslan, Kazim
    In this paper, the curves associated with the Combescure transform are discussed. With the help of the fact that these curves have a common Frenet frame, an equivalence relation is defined. The equivalence classes obtained by this equivalence relation have been examined for some special curves and it has been obtained that all curves in the equivalence class of a helix curve are also helix curves. This is also true for k-slant helix curves. The important part of this paper consists of the useful construction method to obtain a curve from the given curve a with the help of Combescure transformation. With this method, some special curves such as Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve can be obtained from any curve related by a Combescure transform. For example, we obtain an example of Mannheim curves explicitly obtained from an anti-Salkowski curve. It is not easy to find an example of Mannheim curves except circular helix in the literature. In general, the conditions for being Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve of the curve beta obtained from the given curve alpha with the help of Combescure transformation were obtained.