Slant helices in Minkowski 3-space E31 with Sasai’s modified frame fields (original) (raw)

Position Vector of Spacelike Slant Helices in Minkowski 3-SPACE

Honam Mathematical Journal, 2014

In this paper, position vector of a spacelike slant helix with respect to standard frame are deduced in Minkowski space E 3 1. Some new characterizations of a spacelike slant helices are presented. Also, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike curve. In terms of solution, we determine the parametric representation of the spacelike slant helices from the intrinsic equations. Thereafter, we apply this method to find the parametric representation of some special spacelike slant helices such as: Salkowski and anti-Salkowski curves.

Characterizations of Spacelike Slant Helices In Minkowski 3-Space

Annals of the Alexandru Ioan Cuza University - Mathematics, 2014

In this paper, we investigate tangent indicatrix, principal normal indicatrix and binormal indicatrix of a spacelike curve with spacelike, timelike and null principal normal vector in Minkowski 3-space E3 1 and we construct their Frenet equations and curvature functions. Moreover, we obtain some differential equations which characterize for a spacelike curve to be a slant helix by using the Frenet apparatus of spherical indicatrix of the curve. Also related examples and their illustrations are given. Mathematics Subject Classification 2010: 53A04, 53C50.

Characterizations of timelike slant helices in Minkowski 3-space

Mathematical Communications, 2014

In this paper, we investigate the tangent indicatrix, the principal normal indicatrix and the binormal indicatrix of a timelike curve in Minkowski 3-space E 3 1 and we construct their Frenet equations and curvature functions. Moreover, we obtain some differential equations which characterize a timelike curve to be a slant helix by using the Frenet apparatus of a spherical indicatrix of the curve. Also, related examples and their illustrations are given.

On spacelike rectifying slant helices in Minkowski 3-space

TURKISH JOURNAL OF MATHEMATICS, 2018

In this paper, we study the position vector of a spacelike rectifying slant helix with non-lightlike principal normal vector field in E 3 1. First we find the general equations of the curvature and the torsion of spacelike rectifying slant helices. After that, we construct second-order linear differential equations. By their solutions, we determine families of spacelike rectifying slant helices that lie on cones.

Relatively normal-slant helices in Minkowski 333-space

2022

In this paper, we study relatively normal-slant helices lying on timelike as well as spacelike surfaces in Minkowski 333-space $ \mathbb{E}_1^3$. The axes of spacelike and timelike relatively normal-slant helices are obtained via their Darboux frames. We also establish characterization theorems for spacelike and timelike relatively normal-slant helices in Minkowski 333-space mathbbE13\mathbb{E}_1^3mathbbE13. Finally, the relationship between relatively normal-slant helices and slant helices is found on timelike as well as spacelike surfaces.

Null generalized slant helices in Lorentzian space

2014

In this paper, we define a new curve in Lorentzian space which we call null (lightlike) slant helix. We give some characterization of null slant helices in Minkowski 3-space R 3 1 and provide examples which illustrate the results and also we show that there no exists a null slant helix in R 4 1 .

K-type slant helices on spacelike and timelike surfaces

Acta et Commentationes Universitatis Tartuensis de Mathematica

We have derived a necessary and sufficient condition for a non-null normal spacelike curve lying in a spacelike or a timelike surface M ⊂ E13, so that the curve becomes a K-type spacelike slant helix with K ∈ {1,2,3}. We have used Darboux frame to define necessary and sufficient conditions. An example is given for a 1-type spacelike slant helix having a spacelike normal and a timelike binormal.