Results 11 to 20 of about 247 (173)
Direction Curves Associated with Darboux Vectors Fields and Their Characterizations
International Journal of Mathematics and Mathematical Sciences, 2021 In this paper, we consider the Darboux frame of a curve α lying on an arbitrary regular surface and we use its unit osculator Darboux vector D¯o, unit rectifying Darboux vector D¯r, and unit normal Darboux vector D¯n to define some direction curves such ...
Nidal Echabbi, Amina Ouazzani Chahdi
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Characterizations of Unit Darboux Ruled Surface with Quaternions
Journal of New Theory, 2023 This paper presents a quaternionic approach to generating and characterizing the ruled surface drawn by the unit Darboux vector. The study derives the Darboux frame of the surface and relates it to the Frenet frame of the base curve. Moreover, it obtains
Abdussamet Çalışkan
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A new version of energy and elastica for curves with extended darboux frame
Boletim da Sociedade Paranaense de Matemática, 2022 In this work, we research geometrical interpretation involved with the energy by ED-frame field of first and second kind on orientable hypersurface in E⁴. We explore the geometric properties of some graphics by way of energy. We apply totally diverse discussion and approach to illustrate bending energy functional for ED-frame field of first and second ...
Vedat Asil +2 more
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Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$
Journal of New Theory, 2022 In this study, we examine some properties of Salkowski curves in $\mathbb{E}^{3}$. We then make sense of the angle $(nt)$ in the parametric equation of the Salkowski curves.
Mehmet Bektaş +2 more
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Harmonic Evolute Surface of Tubular Surfaces via B-Darboux Frame in Euclidean 3-Space
Advances in Mathematical Physics, 2021 In this article, we look at a surface associated with real-valued functions. The surface is known as a harmonic surface, and its unit normal vector and mean curvature have been used to characterize it. We use the Bishop-Darboux frame (B-Darboux frame) in
E. M. Solouma, Ibrahim AL-Dayel
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Quaternionic Shape Operator and Rotation Matrix on Ruled Surfaces
Axioms, 2023 In this article, we examine the relationship between Darboux frames along parameter curves and the Darboux frame of the base curve of the ruled surface. We derive the equations of the quaternionic shape operators, which can rotate tangent vectors around ...
Yanlin Li, Abdussamet Çalışkan
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TUBULAR SURFACES WITH DARBOUX FRAME IN GALILEAN 3-SPACE [PDF]
Facta Universitatis, Series: Mathematics and Informatics, 2019 In this paper, we define tubular surface by using a Darboux frame instead of a Frenet frame. Subsequently, we compute the Gaussian curvature and the mean curvature of the tubular surface with a Darboux frame. Moreover, we obtain some characterizations for special curves on this tubular surface in a Galilean 3-space.
Kızıltuğ, Sezai +2 more
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Some New Characterizations of The Harmonic and Harmonic 1-Type Curves in Euclidean 3-Space
Foundations of Computing and Decision Sciences, 2021 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.
Samanci Hatice Kuşak +2 more
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Generating Generalized Cylinder with Geodesic Base Curve According to Darboux Frame
Journal of New Theory, 2021 This paper aims to design a generalized cylinder with a geodesic base curve according to the Darboux frame in Euclidean 3-space. A generalized cylinder is a special ruled surface that is constructed by a continuous fixed motion of a generator line called
Nabil Althibany
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Numerical Solution of Differential Equations of Elastic Curves in 3-dimensional Anti-de Sitter Space [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we aim to extend the Darboux frame field into 3-dimensional Anti-de Sitter space and obtain two cases for this extension by considering a parameterized curve on a hypersurface; then we carry out the Euler-Lagrange equations and derive ...
Samira Latifi +2 more
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