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- Title
A New Approach on Type-3 Slant Helix in E<sup>4</sup>.
- Authors
Özdemir, Zehra; Gök, İsmail; Ekmekci, F. Nejat; Yaylı, Yusuf
- Abstract
In this paper, we introduce type-3 slant helix according to parallel transport frame in 4-dimensional Euclidean Space E4 and we use a constant angle φ between a unit and fixed direction vector field X and the last relatively parallel vector field M3 of the curve, that is, <M3, X> = cos φ = const. where <,> is Euclidean inner product. Since the relatively parallel vector field M3 of the curve makes a constant angle with the unit and fixed direction vector field X we call this curve as a type-3 slant helix in 4-dimensional Euclidean Space E4. Also we define new harmonic curvature functions and we give a vector field D which we call Darboux vector field for type-3 slant helix. And then we obtain some characterizations for type-3 slant helix in terms of the harmonic curvature functions and the Darboux vector field D.
- Subjects
HELICES (Algebraic topology); EUCLIDEAN geometry; VECTOR fields; HARMONIC analysis (Mathematics); DARBOUX transformations
- Publication
General Mathematics Notes, 2015, Vol 28, Issue 1, p40
- ISSN
2219-7184
- Publication type
Article