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

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

2009-07-04

arxiv.org/abs/0907.0750v1

Mathematics

Differential Geometry

14 pages, 3 figures

Scientific paper

In classical differential geometry, the problem of the determination of the position vector of an arbitrary space curve according to the intrinsic equations $\kappa=\kappa(s)$ and $\tau=\tau(s)$ (where $\kappa$ and $\tau$ are the curvature and torsion of the space curve $\psi$, 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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