Frenet Apparatus of the Curves and Some Special Curves in the Euclidean 5-Space $E^5$

Abstract

In this study, initially the geometric meanings of the curvatures
of the curves parametrized with the arc length are given in $E^5$.
This is followed by the calculation of the Frenet vectors and
curvatures of any curve. After these, some results have been given
for the state of evolute curve $X$ being a W-curve and the Frenet
vectors and curvatures of involute curve $Y$ have been calculated
in terms of Frenet vectors and curvatures of the curve X. At last,
the differential equation of the spherical curves, the equation of
the radius and the center of the osculating hyperspheres have been
achieved in $E^5$.