Turkish Journal of Mathematics
DOI
10.3906/mat-1908-9
Abstract
In this paper, we define some new vector fields along a space curve with nonvanishing curvatures in Euclidean 4-space. By using these vector fields we determine some new planes, curves, and ruled hypersurfaces. We show that the determined new planes play the role of the Darboux vector. We also show that, contrary to their definitions, osculating curves of the first kind and rectifying curves in Euclidean 4-space can be considered as space curves whose position vectors always lie in a two-dimensional subspace. Furthermore, we construct developable and nondevelopable ruled hypersurfaces associated with the new vector fields in which the base curve is always a geodesic on the developable one.
Keywords
Darboux vector, vector field, ruled hypersurface, geodesic curve
First Page
274
Last Page
283
Recommended Citation
DÜLDÜL, MUSTAFA
(2020)
"Vector fields and planes in $\mathbb{E}^4$ which play the role of Darboux vector,"
Turkish Journal of Mathematics: Vol. 44:
No.
1, Article 18.
https://doi.org/10.3906/mat-1908-9
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss1/18
