Browsing by Author "Kocayigit, H"

Now showing 1 - 20 of 27
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    1-TYPE AND BIHARMONIC FRENET CURVES IN LORENTZIAN 3-SPACE
    Kocayigit, H; Hacisalihoglu, HH
    1-type and biharmonic curves by using Laplace operator in Lorentzian 3-space are studied and some theorems and characterizations are given for these curves.
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    HARMONIC 1-TYPE CURVES AND WEAK BIHARMONIC CURVES IN LORENTZIAN 3-SPACE
    Kocayigit, H; Önder, M; Hacisalihoglu, HH
    In this paper, we give definitions and characterizations of harmonic 1-type and weak biharmonic curves by using the mean curvature vector field of a Frenet curve in the Lorentzian 3-space L-3. We also study weak biharmonic curves whose mean curvature vector fields are in the kernel of normal Laplacian del(perpendicular to). We give some theorems for them in L-3. Moreover, we give some characterizations and results for a Frenet curve in the same space.
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    TIMELIKE HELICES IN THE SEMI-EUCLIDEAN SPACE E24
    Aydin, TA; Ayazoglu, R; Kocayigit, H
    In this paper, we define timelike curves in R-2(4) and characterize such curves in terms of Frenet frame. Also, we examine the timelike helices of R-2(4), taking into account their curvatures. In addition, we study timelike slant helices, timelike B-1-slant helices, timelike B-2-slant helices in four dimensional semi-Euclidean space, R-2(4). And then we obtain an approximate solution for the timelike B-1 slant helix with Taylor matrix collocation method.
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    Some New Characterizations of The Harmonic and Harmonic 1-Type Curves in Euclidean 3-Space
    Samanci, HK; Ayaz, S; Kocayigit, H
    A Laplace operator and harmonic curve have very important uses in various engineering science such as quantum mechanics, wave propagation, diffusion equation for heat, and fluid flow. Additionally, the differential equation characterizations of the harmonic curves play an important role in estimating the geometric properties of these curves. Hence, this paper proposes to compute some new differential equation characterizations of the harmonic curves in Euclidean 3-space by using an alternative frame named the N-Bishop frame. Firstly, we investigated some new differential equation characterizations of the space curves due to the N-Bishop frame. Secondly, we firstly introduced some new space curves which have the harmonic and harmonic 1-type vectors due to alternative frame N-Bishop frame. Finally, we compute new differential equation characterizations using the N-Bishop Darboux and normal Darboux vectors. Thus, using these differential equation characterizations we have proved in which conditions the curve indicates a helix.
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    SOME CHARACTERIZATIONS OF TIMELIKE AND SPACELIKE CURVES WITH HARMONIC 1-TYPE DARBOUX INSTANTANEOUS ROTATION VECTOR IN THE MINKOWSKI 3-SPACE E13
    Kocayigit, H; Önder, M; Arslan, K
    In this study, by using Laplacian and normal Laplacian operators, some characterizations on the Darboux instantaneous rotation vector field of timelike and spacelike curves are given in Minkowski 3-space E-1(3)
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    N-BISHOP DARBOUX VECTOR OF THE SPACELIKE CURVE WITH SPACELIKE BINORMAL
    Samanci, HK; Kocayigit, H
    In this article, the N-Bishop frame in Minkowski space is investigated for space like curves with a spacelike binormial. Some features of the normal expansion are proven via for the spacelike curve. Then, a new Darboux frame called by the N-Bishop Darboux frame is introduced at first time. Furthermore, some geometrical properties of the N-Bishop Darboux frame are proven. As a result, the N-Bishop Darboux axis and momentum rotation vector are calculated.
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    SOME INTEGRAL CHARACTERIZATIONS OF TIMELIKE HELICES IN R42
    Erpehlivan, Z; Kocayigit, H; Aydin, TA
    In this study, we examine timelike helices in R-2(4) and some integral characterizations of these curves in terms of Frenet frame. In addition, we study timelike 2B slant helices in R-2(4) and present the differential equations for vector positions.
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    AN EXPLICIT CHARACTERIZATION OF SPHERICAL CURVES ACCORDING TO BISHOP FRAME AND AN APPROXIMATELY SOLUTION
    Balki Okullu, P; Kocayigit, H; Agirman Aydin, T
    In this paper, spherical curves are studied by using Bishop frame. First, the differential equation characterizing the spherical curves is given. Then, we exhibit that the position vector of a curve which is lying on a sphere satisfies a third-order linear differential equation. Then we solve this linear differential equation by using Bernstein series solution method.
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    Legendre Matrix Method for Legendre Curve in Sasakian 3-Manifold
    Aydin, TA; Sezer, M; Kocayigit, H
    In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.
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    Morgan-Voyce Polynomial Approach for Quaternionic Space Curves of Constant Width
    Aydin, TA; Ayazoglu, R; Kocayigit, H
    The curves of constant width are special curves used in engineering, architecture and technology. In the literature, these curves are considered according to different roofs in different spaces and some integral characterizations of these curves are obtained. However, in order to examine the geometric properties of curves of constant width, more than characterization is required. In this study, firstly differential equations characterizing quaternionic space curves of constant width are obtained. Then, the approximate solutions of the differential equations obtained are calculated by the Morgan-Voyce polynomial approach. The geometric properties of this curve type are examined with the help of these solutions.
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    ON THE SABBAN FRAME BELONGING TO INVOLUTE-EVOLUTE CURVES
    Senyurt, S; Altun, Y; Cevahir, C; Kocayigit, H
    In this paper, we investigate special Smarandache curves with regard to Sabban frame of involute curve. We create Sabban frame belonging to spherical indicatrix of involute curve. Smarandache curves are explained by Sabban vectors belonging to spherical indicatrix. Then, we calculate geodesic curvatures of this Smarandache curves. The results found for each curve is given depending on evolute curve. The example related to the subject is given and their figures are drawn with MAPPLE program.
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    New moving frames for the curves lying on a surface
    Alkan, A; Kocayigit, H; Agirman Aydin, T
    In this article, three new orthogonal frames are defined for the curves lying on a surface. These moving frames, obtained based on the Darboux frame, are called Osculator Darboux Frame, Normal Darboux Frame and Rectifying Darboux Frame, respectively. Also, the Osculator Darboux Frame components and curvatures are calculated for a presented example.
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    1-TYPE CURVES AND BIHARMONIC CURVES IN EUCLIDEAN 3-SPACE
    Kocayigit, H; Hacisalihoglu, HH
    We study 1-type curves by using the mean curvature vector field of the curve. We also study biharmonic curves whose mean curvature vector field is in the kernel of Laplacian. We give some theorems for them in the Euclidean 3-space. Moreover we give some characterizations and results for a Frenet curve in the same space.
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    BIHARMONIC CURVES IN CONTACT GEOMETRY
    Kocayigit, H; Hacisalihoglu, HH
    We study biharmonic curves in contact geometry whose mean curvature vector field is in the kernel of Laplacian. We give some results for biharmonic curves in Sasakian 3-space. We also give some characterizations for Legendre curves in the same space.
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    NATUREL MATES OF EQUIAFFINE SPACE CURVES IN AFFINE 3-SPACE
    Tuncer, Y; Kocayigit, H; Karacan, MK
    In this study, we investigated the natural mates of equiaffine curves with constant equiaffine curvatures, associated to equiaffine frame in affine 3-space and we gave the position vectors under some conditions.
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    SOME SPECIAL CURVES BELONGING TO MANNHEIM CURVES PAIR
    Senyurt, S; Altun, Y; Cevaihr, C; Kocayigit, H
    In this paper, we investigate special Smarandache curves with regard to Sabban frame for Mannheim partner curve spherical indicatrix. We create Sabban frame belonging to this curves. Smarandache curves are explained by taking position vector as Sabban vectors belonging to this curves. Then, we calculate geodesic curvatures of this Smarandache curves. Found results are expressed depending on the Mannheim curve.
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    DIFFERENTIAL REPRESENTATION OF THE LORENTZIAN SPHERICAL TIMELIKE CURVES BY USING BISHOP FRAME
    Balki Okullu, P; Kocayigit, H
    In this study, we will give the differential representation of the Lorentzian spherical timelike curves according to Bishop frame and we obtain a third-order linear differential equation which represents the position vector of a timelike curve lying on a Lorentzian sphere.
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    A STATISTICAL COMPARISON OF ANATOMICAL FEATURES IN SOME Ornithogalum SP SPECIES
    Özdemir, A; Kocayigit, H; Yetisen, K; Akyol, Y; Özdemir, C
    In the present study, Ornithogalum narbonense, O. montanum, O. wiedemannii, O. sigmoideum and O. lanceolatum species were compared statistically with respect to anatomical characters. Some differences were found in root, stem and leaf anatomy of the species. These differences and similarities were indicated in this study. A big metaxylem was present in all root cross sections, except for O. lanceolatum, which has three metaxylema. 2-3 layered annular type collenchyma were present in all species. Aerenchyma is present in all mesophiles.
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    Some new characterizations of a space curve due to a modified frame {(N)over-right-arrow, (C)over-right-arrow, (W)over-right-arrow} in Euclidean 3-space
    Samanci, HK; Ayaz, S; Kocayigit, H
    In our paper, we computed some new characterizations {(N) over right arrow, (C) over right arrow, (W) over right arrow} in Euclidean 3-space and we get general differential equation characterizations of a space curve due to the vectors.(N) over right arrow, (C) over right arrow, (W) over right arrow . Furthermore, we investigated some differential equations characterizations of the harmonic and harmonic 1-type curves.
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    CHARACTERIZATIONS OF SPACE CURVES WITH 1-TYPE DARBOUX INSTANTANEOUS ROTATION VECTOR
    Arslan, K; Kocayigit, H; Önder, M
    In this study, by using Laplace and normal Laplace operators, we give some characterizations for the Darboux instantaneous rotation vector field of the curves in the Euclidean 3-space E-3. Further, we give necessary and sufficient conditions for unit speed space curves to have 1-type Darboux vectors. Moreover, we obtain some characterizations of helices according to Darboux vector.