Inextensible Flows of Spacelike Curves According to Equiform Frame in 4-dimensional Minkowski Space R41

In this paper, we study inextensible flows of spacelike curves lying fully on a spacelike surface Ω according to equiform frame in 4-dimensional Minkowski space ℝ1 4 . We give necessary and sufficient conditions for this inextensible flows which are expressed as a partial differential equation involving the equiform curvature functions in 4-dimensional Minkowski space ℝ1 4 . Finally we give an application of inextensible flows of spacelike curves in ℝ1 4 .

Motions of Curves in 4-Dimensional Galilean Space G4

In this paper, we investigate the flow of curve and its equiform geometry in 4-dimensional Galilean space. We obtain that the Frenet equations and curvatures of inextensible flows of curves and its equiformly invariant vector fields and intrinsic quantities are independent of time. We find that the motions of curves and its equiform geometry can be defined by the inviscid and stochastic Burgers’ equations in 4-dimensional Galilean space.

Tangent bimagnetic curves in terms of inextensible flows in space

In this work, we study inextensible flows of tangent bimagnetic particles in space. Moreover, we obtain the inextensible flows of electric field by Lorentz equation. Finally, we obtain new results for inextensible flows of tangent bimagnetic particles in space.

A new approach for inextensible flows of binormal spherical indicatrices of magnetic curves

In this study, we obtain the special type of magnetic trajectories associated with a magnetic field [Formula: see text] defined on a 3D Riemannian manifold. We investigate a new representation of binormal spherical indicatrices of magnetic curves. Thus, we study [Formula: see text]-magnetic curves terms of inextensible flows. Furthermore, we give some new characterizations of curvatures in terms of some partial differential equations. Finally, we examine some geometrical and physical features of the moving charged particle corresponding to the [Formula: see text]-magnetic curves. Namely, we compute uniformity of the [Formula: see text]-magnetic curves.