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The Spinor Expressions of Mannheim Curves in Euclidean 3-Space
International Electronic Journal of Geometry, 2023In this paper, the spinor formulations of Mannheim curve pair are investigated. First of all, two spinors matching to Mannheim curve pair are given and by considering the relationships between the Frenet frames of Mannheim curve pair, the relationship between two spinors matching to this curve pair are gotten.
Tülay Erişir, Zeynep İsabeyoğlu
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A Remarkable Class of Mannheim-Curves
Canadian Mathematical Bulletin, 1966It is well known that the determination of a (non-isotropic) curve in the euclidean 3-space with given curvature κ(S) and torsion τ(s), where s represents the arc-length, depends upon the integration of a Riccati equation; and that this can be performed only if a particular integral of the equation is known.
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Mannheim partner curves in the special linear group
International Journal of Physical Sciences, 2023 exaly +2 more sources
2020
In the discussion of Bertrand and Mannheim curves, it is always assumed (explicitly or implicitly) that the curvature is nowhere zero. In this paper, we adapt this requirement on the Mannheim curves and investigate into the properties of two types of similar curves (the Frenet-Mannheim curves and the weakened Mannheim curves) under weakened conditions.
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In the discussion of Bertrand and Mannheim curves, it is always assumed (explicitly or implicitly) that the curvature is nowhere zero. In this paper, we adapt this requirement on the Mannheim curves and investigate into the properties of two types of similar curves (the Frenet-Mannheim curves and the weakened Mannheim curves) under weakened conditions.
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Mannheim Curves with Frenet Like Curve (FLC) Frame
2022Eren, Kemal, Soley Ersoy
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Special Partner Curves Derived From Mannheim Partner Curves
2014In this paper, we obtain new partner curves by rotating the Frenet frame of a Mannheim partner curves to an angle of Darboux. We give necessary and sufficient conditions for these new curves to be Mannheim partner curves.
Guler, Fatma +2 more
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Mannheim Partner D Curves in the Euclidean 3 space
2015In this paper, we consider the idea of Mannheim partner curves for curves lying on surfaces. By considering the Darbouxframes of surface curves, we define Mannheim partner D-curves and give the characterizations for these curves. We also find therelations between geodesic curvatures, normal curvatures and geodesic torsions of these associated curves ...
Kazaz, Mustafa +3 more
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Bertrand and Mannheim curves of framed curves in the 4-dimensional Euclidean space
Journal of Geometry, 2023Haiou Yu, Masatomo Takahashi
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