Octonionic curves and their characteristic properties

The Serret-Frenet formula for a curve in the 7 dimensional Euclidean space was reacquired by use of the spatial octonions in the spatial octonionic space O p. The Serret-Frenet formulas for the octonionic curves in the octonionic space O were given by use of the Serret-Frenet formulas obtained. Next, the statements the octonionic inclined curve and the octonionic harmonic curvature for the octonionic curves in the octonionic spaces O p and O were introduced bearing in mind that the Serret-Frenet formulas found for the octonionic curves and the octonionic harmonic curvatures were obtained in terms of the octonionic curvatures of the octonionic curves. Moreover, necessary and sufficient conditions were given to become each of the octonionic curves to the octonionic inclined curves in the octonionic spaces O p and O. Besides, it were shown that the octonionic curve which was obtained from the spatial octonionic inclined curve was a octonionic inclined curve. Finally, the relationships between the octonionic harmonic curvatures of the octonionic curves in the octonionic spaces O p, and O, and curvatures were given.