Yazar "Tosun, Murat" seçeneğine göre listele

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    Bertrand partner P-Trajectories in the Euclidean 3-space e3
    (Ankara Univ, Fac Sci, 2023) Isbilir, Zehra; Ozen, Kahraman Esen; Tosun, Murat
    The concept of a pair of curves, called as Bertrand partner curves, was introduced by Bertrand in 1850. Bertrand partner curves have been stud-ied widely in the literature from past to present. In this study, we take into account of the concept of Bertrand partner trajectories according to Positional Adapted Frame (PAF) for the particles moving in 3-dimensional Euclidean space. Some characterizations are given for these trajectories with the aid of the PAF elements. Then, we obtain some special cases of these trajectories. Moreover, we provide a numerical example.
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    Editorial for special issue IECMSA 2020-International Eurasian Conference on Mathematical Sciences and Applications
    (Wiley, 2022) Tosun, Murat; Kara, Emrah Evren; Usta, Fuat
    [Bastract Not Available]
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    Generalized osculating-type ruled surfaces of singular curves
    (Wiley, 2023) Yazıcı, Bahar Doğan; İşbilir, Zehra; Tosun, Murat
    In this study, we introduce generalized osculating-type ruled surfaces of special singular curves. We give some theories and results about the geometric structure of the surface. In addition, the singular point classes of the surface are examined, and the conditions for being a cross-cap surface are expressed. Generalized osculating-type ruled surface is considered as a framed surface and its basic invariants are found and some results are given. Finally, we give some examples and figures to support the theories.
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    Generalized Rectifying Ruled Surfaces of Special Singular Curves
    (Ovidius Univ Press, 2023) Isbilir, Zehra; Yazici, Bahar Dogan; Tosun, Murat
    In this study, generalized rectifying ruled surfaces of Frenet-type framed base curves in the three-dimensional Euclidean space are introduced. These surfaces are a generalization of not only the tangent and binormal surfaces of Frenet-type framed base curves, but also the tangent and binormal surfaces of regular curves. Additionally, we present some geometric characterizations and properties of these surfaces. Then, the singular point classes of the surface are scrutinized and the conditions for being a cross-cap surface are stated. Moreover, generalized rectifying surfaces are examined as framed surfaces by using the framed surface theory, and we investigate the basic invariants and curvatures of them. Then, several illustrative examples with figures are given to support the theorems and results.
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    MANNHEIM PARTNER P-TRAJECTORIES IN THE EUCLIDEAN 3-SPACE E-3
    (Honam Mathematical Soc, 2022) İşbilir, Zehra; Özen, Kahraman Esen; Tosun, Murat
    Mannheim introduced the concept of a pair of curves, called as Mannheim partner curves, in 1878. Until now, Mannheim partner curves have been studied widely in the literature. In this study, we take into account of this concept according to Positional Adapted Frame (PAF) for the particles moving in the 3-dimensional Euclidean space. We introduce a new type special trajectory pairs which are called Mannheim partner P-trajectories in the Euclidean 3-space. The relationships between the PAF elements of this pair are investigated. Also, the relations between the Serret-Frenet basis vectors of Mannheim partner P-trajectories are given. Afterwards, we obtain the necessary conditions for one of these trajectories to be an osculating curve and for other to be a rectifying curve. Moreover, we provide an example including an illustrative figure.
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    Mannheim partner trajectories related to pafors
    (Univ Nis, 2024) Isbilir, Zehra; Ozen, Kahraman Esen; Tosun, Murat
    In this study, we consider the concept of Mannheim partner trajectories related to the Positional Adapted Frame on Regular Surfaces (PAFORS) for the particles moving on the different regular surfaces in Euclidean 3 -space. We give the relations between the PAFORS elements of these aforementioned trajectories. Also, we obtain the relations between Darboux basis vectors of these trajectories. Furthermore, some special cases of these trajectories are written.
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    A New Insight on Rectifying-Type Curves in Euclidean 4-Space
    (Int Electronic Journal Geometry, 2023) Isbilir, Zehra; Tosun, Murat
    In this study, our purpose is to determine the generalized rectifying-type curves with Frenet-type frame in Myller configuration for Euclidean 4-space E4. Also, some characterizations of them are given. We construct some correlations between curvatures and invariants of generalized rectifyingtype curves. Additionally, we obtain an illustrative example with respect to the rectifying-type curves with Frenet-type frame in Myller configuration for Euclidean 4-space E4.
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    On generalized osculating-type curves in Myller configuration
    (Ovidius Univ Press, 2024) Isbilir, Zehra; Tosun, Murat
    In this study, we examine osculating-type curves with Frenet-type frame in Myller configuration for Euclidean 3-space E-3. We present the necessary characterizations for a curve to be an osculating-type curve. Characterizations originating from the natural structure of Myller configuration are a generalization of osculating curves according to the Frenet frame. Also, we introduce some new results that are not valid for osculating curves. Then, we give an illustrative numerical example supported by a figure.
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    On special curves in Lie groups with Myller configuration
    (Wiley, 2024) Isbilir, Zehra; Dogan Yazici, Bahar; Tosun, Murat
    In this study, we determine a new type comprehensive frame, which is called the generalized Frenet-type frame in three-dimensional Lie groups with Myller configurations, and it includes several special and classical type frames for Euclidean 3-space and three-dimensional Lie groups. After constructing this new comprehensive frame, we obtain derivative formulas with the help of the Lie curvature. In addition, we define some special type curves. The geometry of versor fields along a curve with Frenet-type frame in three-dimensional Lie groups with Myller configurations is a generalization of the usual theory of curves. Since this particular relationship, the osculating-type and rectifying-type curves with Frenet-type frame in three-dimensional Lie groups with Myller configurations include some special cases for osculating and rectifying curves in different spaces.
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    Spinor representation of framed Mannheim curves
    (Scientific and Technological Research Council Turkey, 2022) Doğan Yazıcı, Bahar; İşbilir, Zehra; Tosun, Murat
    In this paper, we obtain spinor with two complex components representations of Mannheim curves of framed curves. Firstly, we give the spinor formulas of the frame corresponding to framed Mannheim curve. Later, we obtain the spinor formulas of the frame corresponding to framed Mannheim partner curve. Moreover, we explain the relationships between spinors corresponding to framed Mannheim pairs and their geometric interpretations. Finally, we present some geometrical results of spinor representations of framed Mannheim curves.
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    The spinor representations of framed Bertrand curves
    (Univ Nis, Fac Sci Math, 2023) İşbilir, Zehra; Yazıcı, Bahar Doğan; Tosun, Murat
    In this study, we intend to examine the framed Bertrand curves in three-dimensional Euclidean space E3 by using the spinors, which have a fundamental place and importance in different disciplines from mathematics to physics. For this purpose, we investigate the spinor representations of framed Bertrand mates in E3. Additionally, we present some geometric results and interpretations. Then, we construct numerical examples with illustrative figures in order to support the given materials.
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    Spinor representations of framed curves in the three-dimensional lie groups
    (Taru Publications, 2023) Isbilir, Zehra; Yazici, Bahar Dogan; Tosun, Murat
    In this study, we determine the spinor representations of special singular curves (framed curves) in the three-dimensional Lie groups with a biinvariant metric. Also, we construct spinor framed equations for some special cases and obtain the relations between the spinor representations of the general frame and adapted frame along the framed curves in the three-dimensional Lie groups. Then, we give some geometric properties and results with respect to them.