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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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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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Bertrand and Mannheim curves of framed curves in the 4-dimensional Euclidean space
Journal of Geometry, 2023Haiou Yu +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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On generalized null Mannheim curves in E24
Mathematical Methods in the Applied Sciences, 2021Nihal Kilic Aslan, KAZIM Ilarslan
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Mannheim Offsets of Dual Curves
Journal of Advanced Research in Pure Mathematics, 2014openaire +1 more source