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    A Proof of an Identity for a Generalization of Well-Known Number Sequences
    (AMER INST PHYSICS, 2015) Yasar, Meral; Bozkurt, Durmus; Yakut, Atakan Tugkan; Simos, TE; Tsitouras, C
    In this study, we give an identity for known special number sequences then prove it using Laplace expansion formula.
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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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    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.
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    The Smarandache Curves on H-0(2)
    (GAZI UNIV, 2016) Savas, Murat; Yakut, Atakan Tugkan; Tamirci, Tugba
    In this study, we give special Smarandache curves according to the Sabban frame in hyperbolic space and new Smarandache partners in de Sitter space. The existence of duality between Smarandache curves in hyperbolic and de Sitter space is obtained. We also describe how we can depict picture of Smarandache partners in de Sitter space of a curve in hyperbolic space. Finally, two examples are given to illustrate our main results.
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    The smarandache curves on H0 2
    (Gazi Universitesi, 2016) Savas, Murat; Yakut, Atakan Tugkan; Tamirci, Tugba
    In this study, we give special Smarandache curves according to the Sabban frame in hyperbolic space and new Smarandache partners in de Sitter space. The existence of duality between Smarandache curves in hyperbolic and de Sitter space is obtained. We also describe how we can depict picture of Smarandache partners in de Sitter space of a curve in hyperbolic space. Finally, two examples are given to illustrate our main results. © 2016 Gazi University Eti Mahallesi. All rights reserved.
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    The Smarandache Curves on S-1(2) and Its Duality on H-0(2)
    (HINDAWI LTD, 2014) Yakut, Atakan Tugkan; Savas, Murat; Tamirci, Tugba
    We introduce special Smarandache curves based on Sabban frame on S-1(2) and we investigate geodesic curvatures of Smarandache curves on de Sitter and hyperbolic spaces. The existence of duality between Smarandache curves on de Sitter space and Smarandache curves on hyperbolic space is shown. Furthermore, we give examples of our main results.