Curves in ${\mathbb R}^ n $ for which the ratios between two consecutive curvatures are
constant are characterized by the fact that their tangent indicatrix is a geodesic in a flat torus …

We study the curve in Rm for which the ratios between two consecutive curvatures are
constant (ccr-curves). We show that closed ccr-curves in Euclidean space Rm are of finite …

In n-dimensional Euclidean space En, harmonic curvatures of a non-degenerate curve
defined by Özdamar and Hacisalihoğlu [Özdamar E, Hacısalihoglu HH. A characterization of …

In n-dimensional Euclidean space En, harmonic curvatures of a non-degenerate curve
defined by Ozdamar and Haci-salihoglu [Ozdamar E, Hacisalihoglu HH. A characterization …

In this work, we study the so-called polynomial general helices in an arbitrary dimensional
Euclidean space. First, we give a method to construct helices from polynomial curves in n …

In this study, we introduce mappings that transform helices in Euclidean n-space to non-null
helices in Minkowski n-space or Minkowski (n+1)-space. Furthermore, we show that these …

In this paper we consider the focal curves of the curves in the Euclidean n-space Rn. First
we give some basic results on Darboux vector of these curves. Later, we prove some results …

General helices that lie on the sphere S in Euclidean space E Page 1 Universal Journal of
Mathematics and Applications, 1 (3) (2018) 166-170 Universal Journal of Mathematics and …

In this work, first, we express some characterizations of helices and ccr curves in the
Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of …

In this paper, we study rectifying curves arising through the dilation of unit speed curves on
the unit sphere S 3 and conclude that arcs of great circles on S 3 do not dilate to rectifying …