Frenet Apparatus of the Curves and Some Special Curves in the Euclidean 5-Space $E^5$ (European Journal of Pure and Applied Mathematics, 2015)
In this study, initially the geometric meanings of the curvaturesof the curves parametrized with the arc length are given in $E^5$.This is followed by the calculation of the Frenet vectors andcurvatures of any curve. After these, some results have been givenfor the state of evolute curve $X$ being a W-curve and the Frenetvectors and curvatures of involute curve $Y$ have been calculatedin terms of Frenet vectors and curvatures of the curve X. At last,the differential equation of the spherical curves, the equation ofthe radius and the center of the osculating hyperspheres have beenachieved in $E^5$.