Since any (arc-length parametrized) space curve is uniquely determined (up to rigid motions) by its curvature  and its torsion . And we knew that a necessary and sufficient condition for a a space curve lies on a sphere is R²+(R')²T²=const , where R=1/κ,T=1/τ,and R' is the derivative of R ralative to s. I want to know if there is a necessary and sufficient condition for a space curve to lie on a ellipsoid(a equation of its curvature and torsion)