Mannheim partner curves in 3-space Page 1 J. Geom. 88 (2008) 120 – 126 0047–2468/08/010120
– 7 © Birkhäuser Verlag, Basel, 2008 DOI 10.1007/s00022-007-1949-0 Mannheim partner …

In this study, we consider framed curves as regular or singular space curves with an adapted
frame in Euclidean 3-space. We define framed natural mates of a framed curve that are …

Rectifying curves are introduced in [2] as space curves whose position vector always lies in
its rectifying plane. In this article, we establish a surprising simple relationship between …

We introduce the notion of the principal (binormal)-direction curve and principal (binormal)-
donor curve of a Frenet curve in E3 and give the relationship of curvature and torsion of its …

Some characterizations of the Euclidean rectifying curves, ie the curves in E3 which have a
property that their position vector always lies in their rectifying plane, are given in [3]. In this …

First, we study rectifying curves via the dilation of unit speed curves on the unit sphere $
S^{2} $ in the Euclidean space $\mathbb E^ 3$. Then we obtain a necessary and sufficient …

The purpose of this report is to give a self-contained survey on null curves in Minkowski 3-
space. This report consists of two parts. In Part I of this report, we give some …

A twisted curve in the Euclidean 3-space $\mathbb E^ 3$ is called a rectifying curve if its
position vector field always lie in its rectifying plane. In this article we study geodesics on an …

The warped product N1× f N2 of two Riemannian manifolds (N1, g1) and (N2, g2) with
warping function f is the product manifold N1× N2 equipped with the warped product metric …

In this paper, we define a rectifying curve in the Euclidean 4-space as a curve whose
position vector always lies in orthogonal complement N^{\perp} of its principal normal vector …