We generalize the Fenchel theorem to strong spacelike (which means that the
tangent vector and the curvature vector span a spacelike 2-plane at each point)
closed curves with index 1 in the 3-dimensional Lorentz space, showing that the
total curvatures must be less than or equal to $2\pi$. A similar generalization
of the Fary-Milnor theorem is also obtained. We establish the Crofton formula
on the de Sitter 2-sphere which implies the above results.Comment: 9 pages, 4 figures. Comments are welcom

Ma, Xiang