Journal ArticleDOI
Mannheim partner curves in 3-space ∗
Huili Liu,Fan Wang +1 more
TLDR
In this paper, the necessary and sufficient conditions for the Mannheim partner curves in Euclidean space and Minkowski space were obtained for three-dimensional space, respectively, and some examples are also given.Abstract:
In this paper, we study Mannheim partner curves in three dimensional space. We obtain the necessary and sufficient conditions for the Mannheim partner curves in Euclidean space $${\mathbb{E}}^{3}$$
and Minkowski space $${\mathbb{E}}^{3}_{1}$$
, respectively. Some examples are also given.read more
Citations
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Journal ArticleDOI
Associated curves of a Frenet curve and their applications
Jin Ho Choi,Young Ho Kim +1 more
TL;DR: The notion of the principal (binormal)-direction curve and principal-donor curve of a Frenet curve in E 3 is introduced and the relationship of curvature and torsion of its mates is given.
Journal ArticleDOI
On Mannheim partner curves in E 3
Keziban Orbay,Emin Kasap +1 more
TL;DR: In this paper, the relationship between the curvatures and the torsions of the Mannheim partner curves with respect to each other was investigated and it was shown that the relationship can be expressed as follows:
Journal ArticleDOI
Mannheim Offsets of Ruled Surfaces
TL;DR: In this paper, Liu and Wang extended the theory of the Mannheim curves to ruled surfaces and defined two ruled surfaces which are offset in the sense of Mannheim, and showed that every developable ruled surface has a Mannheim offset if and only if an equation should be satisfied between the geodesic curvature and the arc length of spherical indicatrix of it.
Tubes with Darboux Frame
Fatih Do ˘ gan,Yusuf Yayli +1 more
TL;DR: In this article, for a center curve C(t) on arbitrary surface M, the authors defined tube with Darboux frame instead of Frenet frame and obtained some characterizations for special curves on this tube.
On mannheim partner curve in dual space
TL;DR: In this paper, the necessary and sufficient conditions for the Mannheim partner curves in dual space D 3 were obtained for three-dimensional dual space and dual space 3D dual space, respectively.
References
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Differential geometry of curves and surfaces
TL;DR: This paper presents a meta-geometry of Surfaces: Isometrics Conformal Maps, which describes how the model derived from the Gauss Map changed over time to reflect the role of curvature in the model construction.
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Semi-Riemannian Geometry With Applications to Relativity
TL;DR: In this article, the authors introduce Semi-Riemannian and Lorenz geometries for manifold theory, including Lie groups and Covering Manifolds, as well as the Calculus of Variations.
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Differential Geometry of Curves and Surfaces
Thomas Banchoff,Stephen Lovett +1 more
TL;DR: In this article, the authors define a set of local properties of a plane, including position, velocity, acceleration, position, acceleration and acceleration, and position, position and acceleration of the plane.
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When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane
TL;DR: 3. S. Thomson, Real Analysis, Prentice Hall, Upper Saddle River, NJ, 1997.
Rectifying curves as centrodes and extremal curves
Bang-Yen Chen,Franki Dillen +1 more
TL;DR: In this paper, it is shown that rectifying curves are extremal curves which satisfy the equality case of a general inequality, and further geometric properties of rectifying curve are also presented.