Abstract: In this work, position vector of a time-like dual curve
according to standard frame of D31
is investigated. First, it is proven
that position vector of a time-like dual curve satisfies a dual vector
differential equation of fourth order. The general solution of this dual
vector differential equation has not yet been found. Due to this, in
terms of special solutions, position vectors of some special time-like
dual curves with respect to standard frame of D31
are 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 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.