Yazar "Yildirim, Mehmet" seçeneğine göre listele

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    An application of Ritt-Wu's zero decomposition algorithm to null Bertrand type curves in Minkowski 3-space
    (Hacettepe Univ, Fac Sci, 2010) Yildirim, Mehmet; Ilarslan, Kazim
    Bertrand curves were first studied using a computer by W. -T. Wu in (A mechanization method of geometry and its applications II. Curve pairs of Bertrand type, Kexue Tongbao 32, 585-588, 1987). The same problem was studied using an improved version of Ritt-Wu's decomposition algorithm by S. -C. Chao and X.-S. Gao (Automated reasoning in differential geometry and mechanics: Part 4: Bertrand curves, System Sciences and Mathematical Sciences 6(2), 186-192, 1993). In this paper, we investigate the same problem for null Bertrand type curves in Minkowski 3-space E-1(3) by using the well known algorithm given by Chao and Gao, and obtain new results for null Bertrand type curves in Minkowski 3-space E-1(3).
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    An application of Ritt-Wu's zero decomposition algorithm to the pseudo null Bertrand type curves in Minkowski 3-space
    (Springer Heidelberg, 2011) Ilarslan, Kazim; Yildirim, Mehmet
    The Bertrand curves were first studied using a computer by Wu (1987). The same problem was studied using an improved version of Ritt-Wu's decomposition algorithm by Chou and Gao (1993). This paper investigates the same problem for pseudo null Bertrand curves in Minkowski 3-space E1(3.)
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    On Darboux helices in Euclidean 4-space
    (Wiley, 2019) Ilarslan, Kazim; Yildirim, Mehmet
    The notion of Darboux helix in Euclidean 3-space was introduced and studied by Yayli et al. 2012. They show that the class of Darboux helices coincide with the class of slant helices. In a special case, if the curvature functions satisfy the equality kappa(2) + tau(2) = constant, then these curves are curve of the constant precession. In this paper, we study Darboux helices in Euclidean 4-space, and we give a characterization for a curve to be a Darboux helix. We also prove that Darboux helices coincide with the general helices. In a special case, if the first and third curvatures of the curve are equal, then Darboux helix, general helix, and V-4-slant helix are the same concepts.
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    On Tensor Product Surfaces of Lorentzian Planar Curves with Pointwise 1-Type Gauss Map
    (Int Electronic Journal Geometry, 2016) Yildirim, Mehmet
    In this article, we study the tensor product surfaces of two Lorentzian planar,non-null curves to have pointwise 1-type Gauss map.
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    ON THE COMPLETE LIFT DISTRIBUTIONS AND THEIR APPLICATIONS TO SEMI-RIEMANNIAN GEOMETRY
    (Int Electronic Journal Geometry, 2010) Yildirim, Mehmet
    In this paper, we investigate the prolongations of the semi-Riemannian distributions to tangent bundle. To achieve this, we define the complete lift of some geometrical objects defined on a given distribution. In addition, we give some general results for the complete lift distribution.
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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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    SEMI-PARALLEL TENSOR PRODUCT SURFACES IN SEMI-EUCLIDEAN SPACE E24
    (Ankara Univ, Fac Sci, 2016) Yildirim, Mehmet; Ilarslan, Kazim
    In this article, the tensor product surfaces are studied that arise from taking the tensor product of a unit circle centered at the origin in Euclidean plane E-2 and a non-null, unit planar curve in Lorentzian plane E-1(2). Also we have shown that the tensor product surfaces in 4-dimensional semi-Euclidean space with index 2, E-2(4), satisfying the semi-parallelity condition (R) over bar (X, Y).h = 0 if and only if the tensor product surface is a totally geodesic surface in E-2(4).