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)