Yazar "Camci, Cetin" seçeneğine göre listele

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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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    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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    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 Method For Construction Of Ph-Helical Curves In E-3
    (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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    New results concerning Cartan null and pseudo null curves in Minkowski 3-space
    (Springer Basel Ag, 2023) Camci, Cetin; Ucum, Ali; Ilarslan, Kazim
    In this study, we focus on Cartan null and pseudo null curves in Minkowski 3-space E-1(3). Firstly we define Cartan null and pseudo null equivalent curves and give the related examples. Then we give a construction method for Cartan null curves and it is shown that every Cartan null curve can be obtained from a timelike curve lying in the Lorentz plane in E-1(3). Also a construction method is given for pseudo null curves and we show that all pseudo null curves lie in a lightlike plane in E-1(3). Finally we define a new surface in E-1(3) called surface of pseudo null curves and we obtain the geometric properties of such surfaces.
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    Sequential natural mates of Frenet curves in Euclidean 3-space
    (Springer Basel Ag, 2021) Camci, Cetin; Chen, Bang-Yen; Ilarslan, Kazim; Ucum, Ali
    Associated with a Frenet curve alpha in Euclidean 3-space E-3, there exists the notion of natural mate beta of alpha. In this article, we extend the natural mate beta to sequential natural mates {alpha(1), alpha(2), . . . , alpha(n alpha)} with alpha(1) = beta. We call each curve alpha(i), i epsilon {1, 2, . . . , n(alpha)}, the i-th natural mate. The main purpose of this article is to study the relationships between the given Frenet curve a with its sequential natural mates {alpha(1), alpha(2), . . . , alpha n(alpha)}.
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    SPACE CURVES RELATED BY A TRANSFORMATION OF COMBESCURE
    (Taylor & Francis Ltd, 2021) Camci, Cetin; Ucum, Ali; Ilarslan, Kazim
    In this paper, the curves associated with the Combescure transform are discussed. With the help of the fact that these curves have a common Frenet frame, an equivalence relation is defined. The equivalence classes obtained by this equivalence relation have been examined for some special curves and it has been obtained that all curves in the equivalence class of a helix curve are also helix curves. This is also true for k-slant helix curves. The important part of this paper consists of the useful construction method to obtain a curve from the given curve a with the help of Combescure transformation. With this method, some special curves such as Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve can be obtained from any curve related by a Combescure transform. For example, we obtain an example of Mannheim curves explicitly obtained from an anti-Salkowski curve. It is not easy to find an example of Mannheim curves except circular helix in the literature. In general, the conditions for being Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve of the curve beta obtained from the given curve alpha with the help of Combescure transformation were obtained.
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    Twisted Surfaces in Semi-Euclidean 4-Space with Index 2
    (Int Electronic Journal Geometry, 2024) Ucum, Ali; Ilarslan, Kazim; Camci, Cetin
    In this paper, we consider the twisted surfaces in semi -Euclidean 4 -space with index 2 . We classify the twisted surface with respect to their spine curve which are non -null or null curves. So, we study the geometric properties of these surfaces. Also we obtain the family of some special surfaces such as flat surfaces, marginally trapped surfaces.