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Mannheim curves and their partner curves in Minkowski 3-space E13
Demonstratio Mathematica, 2022 The modified orthogonal frame is an important tool to study analytic space curves whose curvatures have discrete zero points. In this article, by using the modified orthogonal frame, Mannheim curves and their partner curves are investigated in Minkowski ...
Elsharkawy Ayman, Elshenhab Ahmed M.
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Geometry of coupled dispersionless equations with Mannheim curves
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this paper, a special kind of curve pair associated with each other by the linear dependency between the principal normal vector of the first curve (called Mannheim curve) and the binormal vector of the second curve (called Mannheim partner curve) is ...
Eren Kemal
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Bertrand and Mannheim Curves of Spherical Framed Curves in a Three-Dimensional Sphere
Mathematics, 2022 We investigated differential geometries of Bertrand curves and Mannheim curves in a three-dimensional sphere. We clarify the conditions for regular spherical curves to become Bertrand and Mannheim curves.
Masatomo Takahashi, Haiou Yu
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No Null-Helix Mannheim Curves in the Minkowski Space E13 [PDF]
International Journal of Mathematics and Mathematical Sciences, 2011 We study a null Mannheim curve with time-like or space-like Mannheim partner curve in the Minkowski 3-space E13. We get the characterization of a null Mannheim curve.
Jae Won Lee
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Mannheim Curves in Nonflat 3-Dimensional Space Forms [PDF]
Advances in Mathematical Physics, 2015 We consider the Mannheim curves in nonflat 3-dimensional space forms (Riemannian or Lorentzian) and we give the concept of Mannheim curves. In addition, we investigate the properties of nonnull Mannheim curves and their partner curves.
Wenjing Zhao, Donghe Pei, Xinyu Cao
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MANNHEIM CURVES IN 3-DIMENSIONAL SPACE FORMS [PDF]
Bulletin of the Korean Mathematical Society, 2013 In Euclidean 3-space, Mannheim curves are characterised by the equation \[ \kappa=a(\kappa^2+\tau^2) \] for a constant \(a\neq 0\), where \(\kappa\) and \(\tau\) are the curvature and the torsion of the curve. Similarly, Mannheim partner curves are characterised by \[ \kappa'=\frac{\kappa}{a}(1+a^2\tau^2) \] where \(\kappa'\) represents the derivative ...
Young Ho Kim
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Singular Special Curves in 3-Space Forms
Mathematics, 2020 We study the singular Bertrand curves and Mannheim curves in the 3-dimensional space forms. We introduce the geometrical properties of such special curves.
Jie Huang, Donghe Pei
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Spinor representation of framed Mannheim curves
Turkish Journal of Mathematics, 2022 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.
Zehra Isbilir, Murat Tosun
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On Generalized Spacelike Mannheim Curves in Minkowski Space–Time
Proceedings of the National Academy of Sciences India Section A - Physical Sciences, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
EMILIJA Nešović +2 more
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Bertrand and Mannheim curves of framed curves in the3-dimensional Euclidean space
Turkish Journal of Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shun'Ichi Honda, Masatomo Takahashi
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