Results 1 to 10 of about 61,569 (245)
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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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 ...
Choi, Jin Ho +2 more
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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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Spinor representation of framed Mannheim curves
Turkish Journal of Mathematics, 2022 Summary: 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.
Dogan Yazici, Bahar +2 more
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On Some Quasi-Curves in Galilean Three-Space
Axioms, 2023 In this paper, the quasi-frame and quasi-formulas are introduced in Galilean three-space. In addition, the quasi-Bertrand and the quasi-Mannheim curves are studied.
Ayman Elsharkawy +4 more
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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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Some characterizations of Mannheim partner curves in the Minkowski 3-space E13; pp. 210–220 [PDF]
Proceedings of the Estonian Academy of Sciences, 2011 In this paper, we give some characterizations of Mannheim partner curves in the Minkowski 3-space E13. Firstly, we classify these curves in E13. Next, we give some relationships characterizing these curves and we show that the Mannheim theorem is not ...
Tanju Kahraman +3 more
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Null Darboux Curve Pairs in Minkowski 3-Space
Axioms, 2021 Based on the fundamental theories of null curves in Minkowski 3-space, the null Darboux mate curves of a null curve are defined which can be regarded as a kind of extension for Bertrand curves and Mannheim curves in Minkowski 3-space.
Jinhua Qian +3 more
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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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