Slant helix of order n and sequence of Darboux developables of principal‐directional curves

2020 ◽  
Vol 43 (17) ◽  
pp. 9888-9903
Author(s):  
Yanlin Li ◽  
Zhigang Wang ◽  
Tiehong Zhao
Keyword(s):  
Slant Helix

scholarly journals Special Curves According to Bishop Frame in Minkowski 3-Space

2020 ◽  
Vol 5 (1) ◽  
pp. 237-248
Author(s):  
Muhammad Abubakar Isah ◽  
Mihriban Alyamaç Külahçı
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Bishop Frame ◽  
Null Curve ◽  
Minkowski Spaces ◽  
Slant Helix ◽  
Null Curves ◽  
Necessary And Sufficient

AbstractPseudo null curves were studied by some geometers in both Euclidean and Minkowski spaces, but some special characters of the curve are not considered. In this paper, we study weak AW (k) – type and AW (k) – type pseudo null curve in Minkowski 3-space [E_1^3 . We define helix and slant helix according to Bishop frame in [E_1^3 . Furthermore, the necessary and sufficient conditions for the slant helix and helix in Minkowski 3-space are obtained.

scholarly journals b-Smarandache tm₂ curves of biharmonic new type b-slant helices according to Bishop frame in the Sol space Sol³

2013 ◽  
Vol 31 (2) ◽  
pp. 265
Author(s):  
Talat Körpinar ◽  
Essin Turhan
Keyword(s):  
Type B ◽  
Bishop Frame ◽  
Slant Helix ◽  
New Type ◽  
Sol Space

In this paper, we study b-Smarandache tm₂ curves of biharmonic new type b-slant helix in the Sol³. We characterize the b-Smarandache tm₂ curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric equations in the Sol³.

On slant helix and its spherical indicatrix

2005 ◽  
Vol 169 (1) ◽  
pp. 600-607 ◽  
Author(s):  
L. Kula ◽  
Y. Yayli
Keyword(s):  
Slant Helix ◽  
Spherical Indicatrix

On Curves ofNk–Slant Helix andNk–Constant Precession in Minkowski 3–Space

2014 ◽  
Vol 12 (2) ◽  
pp. 175-189
Author(s):  
Beyhan Uzunoğlu ◽  
Çağla Ramis ◽  
Yusuf Yayli
Keyword(s):  
Slant Helix

scholarly journals A New Approach on Helices in Pseudo-Riemannian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Evren Zıplar ◽  
Yusuf Yaylı ◽  
İsmail Gök
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Riemannian Manifolds ◽  
Frenet Frame ◽  
New Approach ◽  
Nonzero Constant ◽  
Slant Helix

A proper curveαin then-dimensional pseudo-Riemannian manifold(M,g)is called aVn-slant helix if the functiong(Vn,X)is a nonzero constant alongα, whereXis a  parallel vector field alongαandVnisnth Frenet frame. In this work, we study such curves and give important characterizations about them.

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

2014 ◽  
Vol 11 (05) ◽  
pp. 1450045 ◽  
Author(s):  
Mehmet Önder ◽  
Evren Zıplar ◽  
Onur Kaya
Keyword(s):  
Riemannian Manifold ◽  
3 Dimensional ◽  
Slant Helix ◽  
Curvature And Torsion

In this study, we give the definitions and characterizations of Eikonal slant helices, Eikonal Darboux helices and non-modified Eikonal Darboux helices in 3-dimensional Riemannian manifold M3. We show that every Eikonal slant helix is also an Eikonal Darboux helix. Furthermore, we obtain that if the curve α is a non-modified Eikonal Darboux helix, then α is an Eikonal slant helix if and only if κ2 + τ2 = constant, where κ and τ are curvature and torsion of α, respectively.

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