Vn-SLANT HELICES IN MINKOWSKI n-SPACE En1

Abstract

C o m m u n .Fa c .S c i.U n iv .A n k .S e rie s A 1 Vo lu m e 5 8 , N u m b e r 1 , P a g e s 2 9 -3 8 (2 0 0 9 ) IS S N 1 3 0 3 -5 9 9 1 V n SLANT HELICES IN MINKOWSKI n-SPACE E n 1 · ISMAIL GÖK, ÇETIN CAMCI AND H. HILMI HACISALIHO ¼ GLUAbstract. In this paper we give a de…nition of harmonic curvature functions in terms of Vn and de…ne a new kind of slant helix which we call Vn slant helix in n dimensional Minkowski space E n 1 by using the new harmonic curvature functions : Also we de…ne a vector …eld D L which we call Darboux vector …eld of Vn slant helix in n dimensional Minkowski space E n 1 and we give some characterizations about slant helices.

On Darboux helices in Euclidean 4‐space

“…Definition Let be a unit speed curve with nonzero curvatures k i ( i = 1,2,…, n ) in and let { V 1 , V 2 ,…, V n } denote the Frenet frame of the curve α . We call α a V n ‐slant helix, if the n th unit vector field V n makes a constant angle ϕ with a fixed direction X , that is, along the curve, where X is unit vector field in …”

“…Also some characterizations of such curves were presented in other studies . A new kind of a slant helix in Euclidean n‐space , called V n ‐slant helix, is defined and studied in Gök et al They use the constant angle φ in between a fixed direction X and the n th Frenet vector field V n of the curve, that is, φ , and φ = constant.…”

Eikonal slant helices and Eikonal Darboux helices in 3-dimensional Riemannian manifold

“…Furthermore, there exist more special curves in the space such as slant helix which first introduced by Izumiya and Takeuchi by the property that the normal lines of curve make a constant angle with a fixed direction in the Euclidean 3-space 3 E [14]. Slant helices have been studied by some mathematicians and new kinds of these curves also have been introduced [1,11,16,17,19]. Moreover, these curves have been considered in Lorentzian spaces [2,3].…”

On the Quaternionic B 2-Slant Helices in the Euclidean Space E 4

“…They generalized the inclined curves in E 3 to E n , n > 3, and then gave a characterization for them: "If a curve α is an inclined curve then n−2 i=1 H 2 i = constant". And then many studies have been reported on generalized helices, inclined curves by using Hacısalihoglu's harmonic curvature functions [1] , [2] , [3] , [7] .…”

“…In 2008,Önder et al defined a new kind of slant helix in Euclidean 4-space E 4 which they called B 2 -slant helix and they gave some characterizations of this slant helices in Euclidean 4-space E 4 [12] . And then in 2009, Gök et al defined a new kind of slant helix in Euclidean n-space E n , n > 3, which they called V n -slant helix and they gave some characterizations of this slant helices in Euclidean n-space E n [7] .…”