CHARACTERIZATIONS OF HELICES BY USING THEIR DARBOUX VECTORS
Sigma Journal of Engineering and Natural Sciences, vol.38, no.3, pp.1299-1306, 2020 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 38 Issue: 3
- Publication Date: 2020
- Journal Name: Sigma Journal of Engineering and Natural Sciences
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Directory of Open Access Journals
- Page Numbers: pp.1299-1306
- Keywords: curvatures, Darboux vector, generalized helix, slant helix
- Yıldız Technical University Affiliated: Yes
Abstract
In this study, firstly, new proofs of the theorems which characterize the generalized helices, slant helices and relatively-normal slant helices are presented by using the Darboux vectors of these helices. Also, a characterization of a generalized helix lying on an oriented surface is given in terms of its geodesic curvature, geodesic torsion and normal curvature. Secondly, by defining B1-slant helix in Euclidean 4-space, we give its characterization.