in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...

AbstractIntegrable systems are derived from inelastic flows of timelike, spacelike, and null curves in 2– 3– dimensional Minkowski space. The derivation uses a Lorentzian version geometrical moving frame method which is known to yield the modified Korteveg-de Vries (mKdV) equation nonlinear Schrodinger (NLS) Euclidean space, respectively. In 2–dimensional timelike/spacelike curve shown defocusi...

The objective of the study in this paper is to define M₁,M₂-direction curves and M₁,M₂-donor curves of the spacelike curve γ via the Bishop frame of type-2 in E₁³. We obtained the necessary and sufficient conditions when the associated curves to be slant helices and general helices via the Bishop frame of type-2 in E₁³. After defining the spherical indicatrices of the associated curves, we obta...

What is the shape of space in a spacetime? One way of addressing this issue is to consider edgeless spacelike submanifolds of the spacetime. An alternative is to foliate the spacetime by timelike curves and consider the quotient obtained by identifying points on the same timelike curve. In this article we investigate each of these notions and obtain conditions such that it yields a meaningful s...

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...