On focal curves in Euclidean $n$-space $\mathbb{R}^{n}$

Günay Öztürk, Kadri Arslan

In this paper we consider the focal curves of the curves in the Euclidean n-space $\mathbb{R}^{n}.$ First we give some basic results on Darboux vector of these curves. Later, we prove some results on the order of contact of these curves. Further, we give necessary and sufficient conditions for a focal curve to become 2-planar. We also show that if the ratios of the curvatures of a curve $\gamma $ are constant then the ratios of the curvatures of the focal curve $C_{\gamma }$ are also constant.