Results 11 to 20 of about 506,738 (227)
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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Frenet frames and invariants of timelike ruled surfaces
Ain Shams Engineering Journal, 2013 In this study we give the Frenet frames and Frenet invariants of timelike ruled surfaces. We show that a timelike ruled surface and its directing cone have the same base of Frenet frame.
Mehmet Önder, H. Hüseyin Uğurlu
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Journal of Mathematics, 2021 In this study, original definitions of NC−Smarandache ruled surface and NW−Smarandache ruled surface according to the alternative moving frame are introduced in E3.
Soukaina Ouarab
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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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Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in E3
Abstract and Applied Analysis, 2021 In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in E3. It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface.
Soukaina Ouarab
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Abstract and Applied Analysis, 2022 In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in E3. It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface.
Soukaina Ouarab
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Smarandache Ruled Surfaces according to Darboux Frame in E3
Journal of Mathematics, 2021 This paper presents a new approach of constructing special ruled surfaces and aims to study their developability and minimalist conditions. Our concept opens opportunities for application in engineering, surface modeling, and architectural design.
Soukaina Ouarab
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The Cohomological Genus and Symplectic Genus for 4-Manifolds of Rational or Ruled Types
Mathematics, 2021 An important problem in low dimensional topology is to understand the properties of embedded or immersed surfaces in 4-dimensional manifolds. In this article, we estimate the lower genus bound of closed, connected, smoothly embedded, oriented surfaces in
Bo Dai, Chung-I Ho
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Surface Pencil Pair Interpolating Bertrand Pair as Common Asymptotic Curves in Euclidean 3-Space
Mathematics, 2023 In this paper, we obtain the necessary and sufficient conditions of a surface pencil pair interpolating a Bertrand pair as common asymptotic curves in Euclidean 3-space E3.
Fatemah Mofarreh, Rashad A. Abdel-Baky
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Geometry of the normal ruled surfaces
Structural Mechanics of Engineering Constructions and Buildings, 2021 The wide circle of the surfaces formed by the motion of the right line in the normal plain of some base directrix curve is regarded. The generate right line may rotate at some low at the normal plane of the base curve.
Vyacheslav N. Ivanov
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