Yazar "Kaya, Filiz Ertem" seçeneğine göre listele

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    Curve-Surface Pairs on Embedded Surfaces and Involute D-Scroll of the Curve-Surface Pair in E3
    (Mdpi, 2024) Kaya, Filiz Ertem; Senyurt, Suleyman
    Willmore defined embedded surfaces on f:S -> E-3, which is the embedding of S into Euclidean 3-space. He investigated the Euclidean metric of E-3, inducing a Riemannian structure on f(S). The expression analogous to the left-hand member of the curvature K is replaced by the mean curvature H-2 on f(S). Our aim is to observe the Gaussian and mean curvatures of curve-surface pairs using embedded surfaces in different curve-surface pairs and to define some developable operations on their curve-surface pairs. We also investigate the embedded surfaces using the Willmore method. We first recall the Darboux curve-surface and derive the new characterizations. This curve-surface pair is called the osculating Darboux curve-surface if its position vector always lies in the osculating Darboux plane spanned by a Darboux frame. Thus, we observed an osculating Darboux curve-surface pair. We also obtained the D-scroll of the curve-surface pair and involute D-scroll of the curve-surface pair with some differential geometric elements and found D(alpha,M)(s) and D*(alpha,M)(s)-scrolls of the curve-surface pair (alpha,M).
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    DEVELOPABLE CURVE-SURFACE PAIR AND SPHERICAL REPRESENTATIONS BY BISHOP FRAME
    (Ministry Communications & High Technologies Republic Azerbaijan, 2017) Kaya, Filiz Ertem; Yayli, Yusuf
    We know that Izumiya and Takeuchi define slant helices and conical geodesic curves in Euclidean 3-space. They investigated slant helices and geodesic curves. We define new special curve-surface pairs that we call slant helix curve-surface pairs and conical geodesic curve-surface pairs in Euclidean 3-space. The aim of this study is to analyze the curves by using slant helix in type of curve-surface pairs and making some developable operations on their curve-surface pairs well investigate the spherical helix strips by spherical representations by the help of the Bishop frame.
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    Differential Geometric Aspects of Pedal Curves on Surfaces
    (Wiley, 2024) Kaya, Filiz Ertem
    The purpose of this paper is to construct relations and characterizations between the pedal curves and surfaces and to find components of the vector of alpha t by the means of the pedal on the surface M. Also, the formula of pedal curves of a curve alpha is generalized in n-dimensional Euclidean space En. Some special results are obtained within the scope of pedal curves and given with obtained characterization of the pedal curve in n-dimensional space En.
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    Energies with Constant Mean Curvature of Tubular Surfaces by Bishop Frame
    (2021) Kaya, Filiz Ertem
    In this paper Euclidean metric induced by ? : M ? G be the mean curvature of Tubular surfaces by Bishop frame are computed and the curvatures in differential geometry that are soimportant for computing the Helfrich and Willmore energy of the tubular surfaces by bishop frame and giving some theorems are seen. Even though these calculations are very important to prove that the curvatures are very important in differential geometry, in actually these calculations are clearly important as mathematical physics.
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    Gauss, Mean and Total Curvature Formulae of Rational Bezier Curves in Minkowski 4-Space
    (2023) Kaya, Filiz Ertem
    In this paper Gaussian, Mean and total curvature formulae of Rational Bezier Curves with asymptotic frame field are calculated by using its curvatures in 3- dimensional lightlike cone in Minkowski 4- Space. Our main intention is to introduce and investigate some differential geometric properties of the the Rational Bezier Curves with asymptotic frame field in 3- dimensional lightlike cone in Minkowski 4- Space by using its curvatures.
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    Harmonic curvatures of the strip in Minkowski space
    (World Scientific Publ Co Pte Ltd, 2018) Kaya, Filiz Ertem; Yavuz, Ayse
    This study aimed to give definitions and relations between strip theory and harmonic curvatures of the strip in Minkowski space. Previously, the same was done in Euclidean Space (see [F. Ertem Kaya, Y. Yayli and H. H. Hacisalihoglu, A characterization of cylindrical helix strip, Commun. Fac. Sci. Univ. Ank. Ser. A1 59(2) (2010) 37-51]). The present paper gives for the first time a generic characterization of the harmonic curvatures of the strip, helix strip and inclined strip in Minkowski space.
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    Pedal curves obtained from Frenet vector of a space curve and Smarandache curves belonging to these curves
    (Amer Inst Mathematical Sciences-Aims, 2024) Senyurt, Suleyman; Kaya, Filiz Ertem; Canli, Davut
    In this study, first the pedal curves as the geometric locus of perpendicular projections to the Frenet vectors of a space curve were defined and the Frenet vectors, curvature, and torsion of these pedal curves were calculated. Second, for each pedal curve, Smarandache curves were defined by taking the Frenet vectors as position vectors. Finally, the expressions of Frenet vectors, curvature, and torsion related to the main curves were obtained for each Smarandache curve. Thus, new curves were added to the curve family.
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    The Pedal Curves Generated by Alternative Frame Vectors and Their Smarandache Curves
    (Mdpi, 2024) Canli, Davut; Senyurt, Suleyman; Kaya, Filiz Ertem; Grilli, Luca
    In this paper, pedal-like curves are defined resulting from the orthogonal projection of a fixed point on the alternative frame vectors of a given regular curve. For each pedal curve, the Frenet vectors, the curvature and the torsion functions are found to provide the common relations among the main curve and its pedal curves. Then, Smarandache curves are defined by using the alternative frame vectors of each pedal curve as position vectors. The relations of the Frenet apparatus are also established for the pedal curves and their corresponding Smarandache curves. Finally, the expressions of the alternative frame apparatus of each Smarandache curves are given in terms of the alternative frame elements of the pedal curves. Thus, a set of new symmetric curves are introduced that contribute to the vast curve family.
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    Willmore Function on Curvatures of The Curve-Surface Pair Under Mobius Transformation
    (Soc Paranaense Matematica, 2022) Kaya, Filiz Ertem
    We find a geometric invariant of the curve-surface pairs on Willmore functions with the mean and Gauss curvatures. Similar to the work in [5,19], in this work, we define Willmore functions on curve-surface pair and give new characterizations about Willmore functions with necessary and sufficient condition with strip theory in Euclidean 3-space for the first time. In this paper Willmore function on curvatures of the curve-surface pair under Mobius transformation is provided invariant.