New Vector Fields and Planes Obtained by the Extended Darboux Frame Apparatus of the Second Kind

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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 $$W={\tau }_{g}T-{\kappa }_{n}V+{\kappa }_{g}N$$ plays in Euclidean 3-space. Besides, developable and non-developable ruled hypersurfaces associated with these new vector fields are defined.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 24, 2025, Art. #2

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Bahar Uyar Düldül, "New Vector Fields and Planes Obtained by the Extended Darboux Frame Apparatus of the Second Kind," WSEAS Transactions on Mathematics, vol. 24, pp. 8-15, 2025, DOI:10.37394/23206.2025.24.2
Bahar Uyar Düldül. New Vector Fields and Planes Obtained by the Extended Darboux Frame Apparatus of the Second Kind. WSEAS Transactions on Mathematics. 2025;24:8-15. 10.37394/23206.2025.24.2
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