In this present paper, rectifying curves are re-characterized in a shorter and simpler way using harmonic curvatures some relations between focal found terms of their curvature functions $n-$dimensional Euclidean space. Then, Salkowski curve, which is the curve given space investigated. Finally, figures related to theory case $n=3$.

In this study, we consider framed curves as regular or singular space with an adapted frame in Euclidean 3-space. We define natural mates of a curve that are tangent to the generalized principal normal curve. Subsequently, present relationships between and its mates. particular, establish some necessary sufficient conditions for specific curves, such spherical helices, slant rectifying curves. ...

The theory of Finsler metric was introduced by Paul Finsler, in 1918. author defines this using the Minkowski norm instead inner product. Therefore, geometry is a more general and includes Riemannian metric. In present work, metric, we investigate position vector rectifying, normal osculating curves Finslerian 3-space $\mathbb{F}^{3}$. We obtain characterizations these Furthermore, show that re...

A rectifying curve in the Euclidean $n$-space $\mathbb{E}^n$ is defined as an arc-length parametrized $\gamma$ such that its position vector always lies space (i.e., orthogonal complement of principal normal field) $\mathbb{E}^n$. In this paper, analogy to this, we introduce notion $f$-rectifying a by $s$ $f$-position field $\gamma_f$, $\gamma_f(s) = \int f(s) d\gamma$, $\mathbb{E}^n$, where $f...

Framed curves in Euclidean space are used to investigate singular and important for singularity theory. In this study, framed four-dimensional introduced new results obtained. The relation of with Frenet is given Bishop-type frame the help Euler angles. addition, by using space, rectifying curves, osculating normal introduced. Also, some characterizations depending on curvatures

Constructing a surface with geodesic or line of curvature parameterization is an important problem in many practical applications. The present paper aims to design generalized cylinder that parametrized along the geodesics and lines curves Euclidean 3- space. main results show rectifying right respectively.