Browsing by Author "Aydin, TA"

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    TIMELIKE HELICES IN THE SEMI-EUCLIDEAN SPACE E24
    Aydin, TA; Ayazoglu, R; Kocayigit, H
    In this paper, we define timelike curves in R-2(4) and characterize such curves in terms of Frenet frame. Also, we examine the timelike helices of R-2(4), taking into account their curvatures. In addition, we study timelike slant helices, timelike B-1-slant helices, timelike B-2-slant helices in four dimensional semi-Euclidean space, R-2(4). And then we obtain an approximate solution for the timelike B-1 slant helix with Taylor matrix collocation method.
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    SOME INTEGRAL CHARACTERIZATIONS OF TIMELIKE HELICES IN R42
    Erpehlivan, Z; Kocayigit, H; Aydin, TA
    In this study, we examine timelike helices in R-2(4) and some integral characterizations of these curves in terms of Frenet frame. In addition, we study timelike 2B slant helices in R-2(4) and present the differential equations for vector positions.
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    Legendre Matrix Method for Legendre Curve in Sasakian 3-Manifold
    Aydin, TA; Sezer, M; Kocayigit, H
    In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.
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    Morgan-Voyce Polynomial Approach for Quaternionic Space Curves of Constant Width
    Aydin, TA; Ayazoglu, R; Kocayigit, H
    The curves of constant width are special curves used in engineering, architecture and technology. In the literature, these curves are considered according to different roofs in different spaces and some integral characterizations of these curves are obtained. However, in order to examine the geometric properties of curves of constant width, more than characterization is required. In this study, firstly differential equations characterizing quaternionic space curves of constant width are obtained. Then, the approximate solutions of the differential equations obtained are calculated by the Morgan-Voyce polynomial approach. The geometric properties of this curve type are examined with the help of these solutions.
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    SOME SPECIAL SPACELIKE CURVES IN R42
    Aydin, TA; Kocayigit, H
    In this study, we define spacelike curves in R42 and characterize such curves in terms of Frenet frame. Also, we examine some special spacelike curves of R42, taking into account their curvatures. In addition, we study spacelike slant helices, spacelike B2 slant helices in R42. And then we obtain an approximate solution for spacelike-B2 slant helix.