Yazar "Camci, Cetin" seçeneğine göre listele

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    A new approach to Bertrand curves in Euclidean 3-space
    (Springer Basel Ag, 2020) Camci, Cetin; Ucum, Ali; Ilarslan, Kazim
    In this article, a new approach is given for Bertrand curves in 3-dimensional Euclidean space. According to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Bertrand curve in E-3. In addition, the related examples and graphs are given by showing that general helices and anti-Salkowski curves can be Bertrand curves or their mates, which is their new characterization.
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    A New Class of Bertrand Curves in Euclidean 4-Space
    (Mdpi, 2022) Li, Yanlin; Ucum, Ali; Ilarslan, Kazim; Camci, Cetin
    Bertrand curves are a pair of curves that have a common principal normal vector at any point and are related to symmetry properties. In the present paper, we define the notion of (1, 3)-V Bertrand curves in Euclidean 4-space. Then we find the necessary and sufficient conditions for curves in Euclidean 4-space to be (1, 3)-V Bertrand curves. Some related examples are given.
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    A NEW METHOD FOR CONSTRUCTION OF PH-HELICAL CURVES IN E3
    (Publ House Bulgarian Acad Sci, 2019) Camci, Cetin; Ilarslan, Kazim
    Helices curves are characterized by the property that their unit tangents maintain a constant inclination with respect to a fixed line, the axis of the helix. If a polynomial space curve is helical, it must be a Pythagorean-hodograph PH-curve. In this paper, a method for constructing PH-helices in 3-dimensional Euclidean space E-3 is proposed, based on a method given by IZUMIYA and TAKEUCHI [(9)] for helices and Bertrand curves in 3-dimensional Euclidean space. We show that the method is true for the polynomial space curves to be PH-helix if the planar curve is a polynomial curve. We also obtain all planar polynomial curve in E-3. We give a new method to construct PH-helices from planar polynomial curves.
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    A NEW TYPE WARPED PRODUCT METRIC IN CONTACT GEOMETRY
    (Honam Mathematical Soc, 2022) Mollaogullari, Ahmet; Camci, Cetin
    This study presents an alpha-Sasakian structure on the product manifold M-1 x beta (I) , where M-1 is a Kahler manifold with an exact 1-form, and beta(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.
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    Characterizations of the position vector of a surface curve in Euclidean 3-space
    (Ovidius Univ Press, 2011) Camci, Cetin; Kula, Levent; Ilarslan, Kazim
    In this paper, we give some characterizations of position vector of a unit speed curve in a regular surface M subset of E-3 which always lies in the planes spanned by {T, Z}, {T, Y} and {Y, Z}, respectively, by using (curve-surface)-frame {T,Y,Z} instead of Frenet frame {T, N, B}. We characterize such curves in terms of the geodesic curvature k(g), normal curvature k(n) and geodesic torsion t(r). Furthermore, we give some characterization for the regular surface M by using the concept of transversality of surfaces in Euclidean 3-space.
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    Equivalent curves in En
    (Amer Inst Mathematical Sciences-Aims, 2025) Mollaogullari, Ahmet; Gumus, Mehmet; Camci, Didem Karalarlioglu; Ilarslan, Kazim; Camci, Cetin
    In this paper, we first define an equivalence relation for curves in En. Based on this equivalence relation, we investigate the relationships between the Frenet frame and curvatures of equivalent curves. Next, we introduce the concept of linearly dependent curvatures in Enand examine its implications for equivalent curves. Building on this concept and the proposed equivalence relation, we present a method to construct (1,3)-Bertrand curves in E4. Additionally, we derive the relationships between the harmonic curvatures of equivalent curves and use these relationships to establish several properties of equivalent helical curves. These results enable systematic construction of curves with prescribed geometric properties.
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    Extended cross product in a 3-dimensional almost contact metric manifold with applications to curve theory
    (Tubitak Scientific & Technological Research Council Turkey, 2012) Camci, Cetin
    In this work, we define a new cross product in 3-dimensional almost contact metric manifold and we study the theory of curves using this new cross product in this manifold. Besides, in the works of Baikousis, Blair [1] and Cho et al. [4], we observe that some theorems are incomplete and excessively generalized are thus their alternative proofs presented.
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    FINITE TYPE CURVE IN 3-DIMENSIONAL SASAKIAN MANIFOLD
    (Korean Mathematical Soc, 2010) Camci, Cetin; Hacisalihoglu, H. Hilmi
    We study finite type curve in R(3)(-3) which lies in a cylinder N(2)(c). Baikousis and Blair proved that a Legendre curve in R(3)(-3) of constant curvature lies in cylinder N(2)(c) and is a 1-type curve, conversely, a 1-type Legendre curve is of constant curvature. In this paper, we will prove that a 1-type curve lying in a cylinder N(2)(c) has a constant curvature. Furthermore we will prove that a curve in R(3)(-3) which lies in a cylinder N(2)(c) is finite type if and only if the curve is 1-type.
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    General Helices with Lightlike Slope Axis
    (Univ Nis, Fac Sci Math, 2018) Camci, Cetin; Ilarslan, Kazim; Ucum, Ali
    In this paper, we investigate general helices with lightlike slope axis. We give necessary and sufficient conditions for a general helix to have a lightlike slope axis. We obtain parametric equation of all general helices with lightlike slope axis. Also we give a nice relation between helix with lightlike slope axis and biharmonic curves in Minkowski 3-space E-1(3).
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    General helices with spacelike slope axis in Minkowski 3-space
    (World Scientific Publ Co Pte Ltd, 2019) Ucum, Ad; Camci, Cetin; Ilarslan, Kazim
    In the present paper, we consider general helix with spacelike slope axis for all possible types of curves in Minkowski 3-space. We give the conditions under which the curves in Minkowski 3-space have spacelike slope axis. In addition, we find the parametric equations of the curves. Also, we give the related examples and their graphics.
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    General Helices with Timelike Slope Axis in Minkowski 3-Space
    (Springer Basel Ag, 2016) Ucum, Ali; Camci, Cetin; Ilarslan, Kazim
    In the present paper, we consider the general helices in Minkowski 3-space to have a constant timelike slope axis. As a result, we show that there exists no pseudo null helix with constant timelike slope axis or spacelike helix with timelike principal normal and constant timelike slope axis. Moreover, we obtain the parametric equations of spacelike helix with spacelike principal normal, timelike helix and null Cartan helix with timelike slope axis. We also give some related examples and their figures.
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    Harmonic curvatures and generalized helices in En
    (Pergamon-Elsevier Science Ltd, 2009) Camci, Cetin; Ilarslan, Kazim; Kula, Levent; Hacisalihoglu, H. Hilmi
    In n-dimensional Euclidean space E-n, harmonic curvatures of a non-degenerate curve defined by Ozdamar and Haci-salihoglu [Ozdamar E, Hacisalihoglu HH. A characterization of Inclined curves in Euclidean n-space. Comm Fac Sci Univ Ankara, Ser A 1 1975;24:15-23]. In this paper, we give some characterizations for a non-degenerate curve alpha to be a generalized helix by using its harmonic curvatures. Also we define the generalized Darboux vector D of a non-degenerate curve alpha in n-dimensional Euclidean space E-n and we show that the generalized Darboux vector D lies in the kernel of Frenet matrix M(s) if and only if the curve a is a generalized helix in the sense of Hayden. (C) 2007 Elsevier Ltd. All rights reserved.
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    ON SURFACE THEORY IN 3-DIMENSIONAL ALMOST CONTACT METRIC MANIFOLD
    (Ankara Univ, Fac Sci, 2011) Gok, Ismail; Camci, Cetin; Hacisalihoglu, H. Hilmi
    In this paper, we study surface theory in 3-dimensional almost contact metric manifolds by using cross product defined by Camci [6] . Camci also studied the theory of curves using the new cross product on this manifolds. In this study, we have defined unit normal vector field of any surface in R-3 (-3) and then, we investigate shape operator matrix of the surface. Morever, we calculate the formulas of Gaussian and mean curvatures of a surface in R-3 (-3).
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    Vn- SLANT HELICES IN MINKOWSKI n-SPACE E1n
    (Ankara Univ, Fac Sci, 2009) Gok, Ismail; Camci, Cetin; Hacisalihoglu, H. Hilmi
    In this paper we give a definition of harmonic curvature functions in terms of V-n and define a new kind of slant helix which we call V-n-slant helix in n-dimensional Minkowski space E-1(n) by using the new harmonic curvature functions . Also we define a vector field D-L which we call Darboux vector field of V-n-slant helix in n-dimensional Minkowski space E-1(n) and we give some characterizations about slant helices.
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    Vn-slant helices in Euclidean n-space En
    (Univ Osijek, Dept Mathematics, 2009) Gok, Ismail; Camci, Cetin; Hacisalihoglu, H. Hilmi
    In this paper, we give a definition of harmonic curvature functions in terms of V-n and we define a new kind of a slant helix. We call this new slant helix a V-n-slant helix in n-dimensional Euclidean space En and define it by using new harmonic curvature functions. We also de fine a vector field D which we call a Darboux vector field of a Vn-slant helix in n-dimensional Euclidean space En and we give a new characterization as: alpha : I subset of R -> E-n is a V-n-slant helix <-> Hn-2*' - k1H(n-3)* = 0, where Hn-2*, Hn-3* are harmonic curvature functions and k(1) shows the first curvature function of the curve alpha.