Framed curves in Euclidean space are used to investigate singular and important for singularity theory. In this study, framed four-dimensional introduced new results obtained. The relation of with Frenet is given Bishop-type frame the help Euler angles. addition, by using space, rectifying curves, osculating normal introduced. Also, some characterizations depending on curvatures

In the present paper, we investigate differential geometric properties soliton surface $M$ associated with Betchov-Da Rios equation. Then, give derivative formulas of Frenet frame unit speed curve $\Phi=\Phi(s,t)$ for all $t$. Also, discuss linear map Weingarten type in tangent space that generates two invariants: $k$ and $h$. Moreover, obtain necessary sufficient conditions equation to be a mi...

Curves as a subject of differential geometry have been intriguing for researchers throughout mathematical history and so they have been one of the interesting research fields. Regular curves play a central role in the theory of curves in differential geometry. In the theory of curves, there are some special curves such as Bertrand curves, Mannheim curves, involute and evolute curves, and pedal ...

The aim of this paper is to determine Frenet-Serret invariants of non-null curves in Lorentzian 5-space. First, we define a vector product of four vectors, by this way, we present a method to calculate Frenet-Serret invariants of the non-null curves. Additionally, an algebraic example of presented method is illustrated. Keywords—Lorentzian 5-space; Frenet-Serret Invariants; Nonnull Curves.

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...

This work presents a robust constrained path-following control scheme for the unmanned aerial vehicle (UAV) under wind disturbances. Through appointing projection from UAV to path, Serret–Frenet frame is introduced reduce complexity of problem. Specifically, disturbance interval observer employed generate Then, design presented based on dynamic surface technique, and auxiliary system adopted de...

The Differential Geometry of curves is described by means of the Frenet-Serret formulas, which cast first, second and third order derivatives into curvature and torsion. While in usual vector calculus these quantities are usually considered to be scalar values, formulating the Frenet-Serret equations in the framework of Geometric Algebra exhibits that they are best described by a bivector for t...

This survey presents an overview to various types of continuity of curves and surfaces, in particular parametric (C n), visual or geometric (V n , G n), Frenet frame (F n), and tangent surface continuity (T n), and discusses the relation with curve and surface modeling, visibility of (dis)continuities, and graphics rendering algorithms. It is the purpose of this paper to provide an overview of ...

We consider the Laplace operator in a thin tube of R with a Dirichlet condition on its boundary. We study asymptotically the spectrum of such an operator as the thickness of the tube’s cross section goes to zero. In particular we analyse how the energy levels depend simultaneously on the curvature of the tube’s central axis and on the rotation of the cross section with respect to the Frenet fra...