In this study, the parametric equation of hypersurfaces passing through spacelike and timelike curves that has non-null Frenet vectors in E_1^4 Lorentz Minkowski space was expressed with help curve is frame. Furthermore, hypersurface families were created by giving necessary sufficient conditions so on common isoasymptotic hypersurface. Then, these obtained deviation marching-scale functions si...

In this work, we firstly introduce notions of principal directed curves and donor which are associated a Frenet curve in the dual Lorentzian space D 3 1 D13 . We give some relations between curvature torsion curve. show that general helix is plane obtain equation by using position vector Then circle $\mathbb{D}^{2}$ or hyperbola $\mathbb{D}_{1}^{2}$ slant $\mathbb{D}_{1}^{3}$ helix, respectivel...

We construct a static axisymmetric wormhole from the gravitational field of two charged shells which are kept in equilibrium by their electromagnetic repulsion. For large separations the exterior tends to the Majumdar-Papapetrou spacetime of two charged particles. The interior of the wormhole is a Reissner-Nordström black hole matching to the two shells. The wormhole is traversable and connects...

In this work we study spacelike and timelike surfaces of revolution in Minkowski space E1 that satisfy the linear Weingarten relation aH+bK = c, where H and K denote the mean curvature and the Gauss curvature of the surface and a, b and c are constants. The classification depends on the causal character of the axis of revolution. We will give a first integral of the equation of the generating c...

In this paper, the stationary acceleration of the spherical general helix in a 3-dimensional Lie group is studied by using a bi-invariant metric. The relationship between the Frenet elements of the stationary acceleration curve in 4-dimensional Euclidean space and the intrinsic Frenet elements of the Lie group is outlined. As a consequence, the corresponding curvature and torsion of these curve...

Given any (topological) Cauchy hypersurface S of a globally hyperbolic spacetime, we construct a smooth function τ : M → R such that the levels St = τ (t), t ∈ R satisfy: (i) S = S0, (ii) each t ∈ R\{0} is a (smooth) spacelike Cauchy hypersurface. If S is also acausal (and not only achronal) then the smooth function τ becomes a time function, i.e., it is strictly increasing on any future-direct...

Abstract In this paper, we study the vortex filament flow for timelike and spacelike curves in Minkowski 3-space. The equations of are equivalent to nonlinear Schrödinger equation heat equation, respectively. As a consequentce, prove that soliton curve gives solution traveling wave on line at infinity. Also, terms new complex frame. Finally, discuss method find exact shape from by solving Frene...