Geodesic
On focal curves in Euclidean $n$-space $\mathbb{R}^{n}$
Novi Sad Journal of Mathematics, Tome 46 (2016) no. 1 Cet article a éte moissonné depuis la source Novi sad journal of mathematics website

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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.
Publié le :
DOI : 10.30755/NSJOM.2013.058
Classification : 53A04, 53C42
Keywords: Frenet curve, Darboux vector, focal curve, normal section 
@article{10.30755/NSJOM.2013.058,
     author = {G\"unay \"Ozt\"urk and Kadri Arslan},
     title = {On focal curves in {Euclidean} $n$-space $\mathbb{R}^{n}$},
     journal = {Novi Sad Journal of Mathematics},
     pages = {35 - 44},
     year = {2016},
     volume = {46},
     number = {1},
     doi = {10.30755/NSJOM.2013.058},
     url = {http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.2013.058/}
}
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Günay Öztürk; Kadri Arslan. On focal curves in Euclidean $n$-space $\mathbb{R}^{n}$. Novi Sad Journal of Mathematics, Tome 46 (2016) no. 1. doi: 10.30755/NSJOM.2013.058

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