A necessary and sufficient condition for the closed trajectories of a rational flow on a standard torus in Euclidean 3-space is given in order to have non-vanishing torsion. These conditions are used to establish examples of closed curves in Euclidean n-space having non-vanishing curvatures up to the highest order. Furthermore a detailed survey is given on results concerning the minimal number of stationary osculating planes for closed curves in 3-space. The author proves such a kind of four-vertex-theorem for multiple graphs on a straight circular cylinder in 3-space.