Some characterization of curves of constant breadth in \(E^n\) space (Q2770957)

If for a simple closed curve in Euclidean space \(E^n\) the normal hyperplane at a point \(P\) meets the curve at a single point \(Q\) the latter is called the opposite point of \(P\). If the distance between opposite points is constant the curve is said to be of constant breadth. Previously such kind of curves have been studied for \(n\leq 4\) [see e.g. \textit{A. Magden} and \textit{Ö. Köse}, Turk. J. Math. 21, 277-284 (1997; Zbl 0937.53004)]. Now for an arbitrary \(n\) a system of equations is deduced which describes these curves. Also some kind of solution of this system is obtained. An integral equality is given connecting the curvatures of the curve.