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Full-Text Articles in Physical Sciences and Mathematics
Characterizations Of Dual Curves And Dual Focal Curves In Dual Lorentzian Space $ D^{3}_{1} $, Sareh Mehdizadeh Gilani, Nemat Abazari, Yusuf Yayli
Characterizations Of Dual Curves And Dual Focal Curves In Dual Lorentzian Space $ D^{3}_{1} $, Sareh Mehdizadeh Gilani, Nemat Abazari, Yusuf Yayli
Turkish Journal of Mathematics
In this paper, we have introduced dual Lorentzian connection, bracket and curvature tensor on dual Lorentzian space $ D_{1}^{3} .$ We have studied a dual curve in different situations in dual Lorentzian space $D^{3}_{1} $ and have found Bishop Darboux vector and some relations according to this vector field, Bishop frame and focal curve of the present dual curve. It has been shown that Bishop Darboux vector has a similar amount in three different cases of a dual curve and the first dual focal curvature of the aforementioned curve is constant function.
Vector Fields And Planes In $\Mathbb{E}^4$ Which Play The Role Of Darboux Vector, Mustafa Düldül
Vector Fields And Planes In $\Mathbb{E}^4$ Which Play The Role Of Darboux Vector, Mustafa Düldül
Turkish Journal of Mathematics
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 …