Extension of the Darboux frame into Euclidean 4-space and its invariants | Zendy

Mustafa Düldül | Zendy; Bahar Uyar Düldül | Zendy; N. Kuruoğlu | Zendy; E. ÖZDAMAR | Zendy

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Extension of the Darboux frame into Euclidean 4-space and its invariants

Author(s) -

Mustafa Düldül,

Bahar Uyar Düldül,

N. Kuruoğlu,

E. ÖZDAMAR

Publication year - 2017

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1604-56

Subject(s) - frenet–serret formulas , hypersurface , mathematics , euclidean geometry , extension (predicate logic) , curvature , frame (networking) , euclidean space , vector field , mathematical analysis , pure mathematics , moving frame , geometry , computer science , telecommunications , programming language

In this paper, by considering a Frenet curve lying on an oriented hypersurface, we extend the Darboux frame field into Euclidean 4-space E . Depending on the linear independency of the curvature vector with the hypersurface’s normal, we obtain two cases for this extension. For each case, we obtain some geometrical meanings of new invariants along the curve on the hypersurface. We also give the relationships between the Frenet frame curvatures and Darboux frame curvatures in E . Finally, we compute the expressions of the new invariants of a Frenet curve lying on an implicit hypersurface.

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