WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
New Vector Fields and Planes Obtained by the Extended Darboux Frame Apparatus of the Second Kind
Author:
Abstract: In this paper, new vector fields are defined along a curve lying on an orientable hypersurface with nonvanishing extended Darboux curvatures of the second kind, and some new planes and curves are introduced using these vector fields in Euclidean 4-space. It is also shown that in 4-dimensional space, these new planes play the same role that the Darboux vector $$W=τ_{g}T-κ_{n} V+κ_{g}N$$ plays in Euclidean 3-space. Besides, developable and non-developable ruled hypersurfaces associated with these new vector fields are defined.