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: 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: 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.