Some characterizations of dual vector fields

The set of the dual vectors which are introduced by $vec{A}=vec{a}+varepsilonvec{a^{*}}$, $varepsilon^{2}=0$ called as "dual vector field". In our paper, we introduce the directional derivative of the dual vector fields and investigate some properties of them. Then we give a numeric example of the dual vector field aided by E.Study theorem.