Dual quaternions and dual quaternionic curves

First of all, basic concept about 3 and 4-dimensional Galilean space is given. Besides some basic definitions about dual quaternions, multiplication of dual quaternions reviewed including multiplication of pure dual quaternions. Hence, an isomorphic structure with Galilean space has been established. Thus, as a result of the isomorphic structure, Serret-Frenet formulae for dual quaternionic curves and Frenet elements are obtained.