Abstract: 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.
Abstract: These In this work, a regular unit speed curve in six
dimensional Euclidean space, whose Frenet curvatures are constant,
is considered. Thereafter, a method to calculate Frenet apparatus of
this curve is presented.
Abstract: In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.
Abstract: In the first part of this paper [6], a method to
determine Frenet apparatus of the space-like curves in Minkowski
space-time is presented. In this work, the mentioned method is
developed for the time-like curves in Minkowski space-time.
Additionally, an example of presented method is illustrated.
Abstract: The curves, of which the square of the distance
between the two points equal to zero, are called minimal or isotropic
curves [4]. In this work, first, necessary and sufficient conditions to
be a Pseudo Helix, which is a special case of such curves, are
presented. Thereafter, it is proven that an isotropic curve-s position
vector and pseudo curvature satisfy a vector differential equation of
fourth order. Additionally, In view of solution of mentioned
equation, position vector of pseudo helices is obtained.
Abstract: In this paper, first, a characterization of spherical
Pseudo null curves in Semi-Euclidean space is given. Then, to
investigate position vector of a pseudo null curve, a system of
differential equation whose solution gives the components of the
position vector of a pseudo null curve on the Frenet axis is
established by means of Frenet equations. Additionally, in view of
some special solutions of mentioned system, characterizations of
some special pseudo null curves are presented.