Yazar "Kizilay, Alperen" seçeneğine göre listele

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    A WORK ON INEXTENSIBLE FLOWS OF SPACE CURVES WITH RESPECT TO A NEW ORTHOGONAL FRAME IN E3
    (Honam Mathematical Soc, 2023) Kizilay, Alperen; Yakut, Atakan Tugkan
    In this study, we bring forth a new general formula for inex-tensible flows of Euclidean curves as regards modified orthogonal frame (MOF) in E3. For an inextensible curve flow, we provide the neces-sary and sufficient conditions, which are denoted by a partial differential equality containing the curvatures and torsion.
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    Evolution of quaternionic curve in the semi-Euclidean space E24
    (Wiley, 2021) Kizilay, Alperen; Yildiz, Onder Gokmen; Okuyucu, Osman Zeki
    In this paper, kinematics of semi-real quaternionic curve in semi-Euclidean space E24 is obtained in terms of its curvature functions. The evolution equation of Frenet frame and curvatures of quaternionic curve are obtained. Also, examples of evolution equations of curvatures are given.
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    Inextensible Flows of Space Curves According to a New Orthogonal Frame with Curvature in E3 1
    (Int Electronic Journal Geometry, 2023) Kizilay, Alperen; Yakut, Atakan Tugkan
    The aim of this paper is to calculate inextensible curve flow using a new orthogonal frame in three-dimensional Minkowski space. First, the history of the subject the main geometric results are presented. Then we obtain inextensible flow of Frenet frame and curvatures. Last, the necessary and sufficient conditions for inextensible curve flow are given by a partial differential equation (PDE) which is involve curvature.
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    On the curve evolution with a new modified orthogonal Saban frame
    (Amer Inst Mathematical Sciences-Aims, 2024) Yakut, Atakan Tugkan; Kizilay, Alperen
    The flow of a curve is said to be inextensible if the arc length in the first case and the intrinsic curvature in the second case are preserved. In this work, we investigated the inextensible flow of a curve on S2 2 according to a modified orthogonal Saban frame. Initially, we gave the definition of the modified Saban frame and then established the relations between the Frenet and the modified orthogonal Saban frames. Later, we determined the inextensible curve flow and geodesic curvature of a curve on the unit sphere using the modified orthogonal Saban frame. Also, we gave some theorems and results for special cases of the evolution of a curve on a sphere. Finally, we gave examples and their graphs for the inextensible flow equation of curvatures.