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arXiv · 0907.0750

Position vectors of slant helices in Euclidean space E$^3$

Ahmad T Ali
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Abstract

In classical differential geometry, the problem of the determination of the position vector of an arbitrary space curve according to the intrinsic equations $κ=κ(s)$ and $τ=τ(s)$ (where $κ$ and $τ$ are the curvature and torsion of the space curve $ψ$, respectively) is still open \cite{eisenh, lips}. However, in the case of a plane curve, helix and general helix, this problem is solved. In this paper, we solved this problem in the case of a slant helix. Also, we applied this method to find the representation of a Salkowski, anti-Salkowski curves and a curve of constant precession, as examples of a slant helices, by means of intrinsic equations.

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Ahmad T Ali. 2009-07-04. Position vectors of slant helices in Euclidean space E$^3$. https://arxiv.org/abs/0907.0750

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