Associated curves bring meaningful geometric expression to the physics and mathematics fields in characterization of surfaces created by those curves, their behavior, study particle motion space-time. In this work, we examine relationship between adjoint focal which are two important examples associated curves. We do review for spacelike under quasi(q)-frame 3D Minkowski space. To put it more c...

In this paper, we get the time evolution equations of curvature and torsion evolving spacelike curves in Minkowski space. Also, give inextensible evolutions timelike ruled surfaces that are produced by normal binormal vector fields curve derive necessary conditions for an inelastic surface evolution. Then, compute coefficients first second fundamental forms, Gauss mean curvatures special surfac...

For a compact spacelike constant mean curvature surface with nonempty boundary in the threedimensional Lorentz–Minkowski space, we introduce a rotation index of the lines of curvature at the boundary umbilical point, which was developed by Choe [‘Sufficient conditions for constant mean curvature surfaces to be round’, Math. Ann. 323(1) (2002), 143–156]. Using the concept of the rotation index a...

In this paper, we analyze involutes of pseudo-null curves in Lorentz–Minkowski 3-space. Pseudo-null are spacelike with null principal normals, and their can be defined analogously as for the Euclidean curves, but they exhibit properties that cannot occur space. The first result paper is more precisely, straight lines. Furthermore, a method reconstruction curve from given line its involute provi...

In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

The black hole singularity plays a crucial role in formulating Hawking's information paradox. global spacetime analysis may be reconciled with unitarity by imposing final state boundary condition on the spacelike singularity. Motivated proposal, we explore effect of projection two dimensional conformal field theories. We calculate time evolution under postselection employing real part pseudoent...

The approach of the paper is on spacelike circular surfaces in Minkowski 3-space. A surface a one-parameter family Lorentzian circles with fixed radius regarding non-null curve, which acts as spine and it has symmetrical properties. In study, we have parametrized provided their geometric singularity properties such Gaussian mean curvatures, comparing them those ruled classification singularitie...

Given a globally hyperbolic spacetime, the existence of a (smooth) spacelike Cauchy hypersurface S has been proven recently. Here, we prove that any acausal spacelike compact submanifold with boundary can be smoothly extended to a spacelike Cauchy hypersurface. Apart from the interest as a purely geometric question (applicable to the Cauchy problem in General Relativity), the result is motivate...