Null hypersurfaces in Lorentzian manifolds with the null energy condition.

We define light-like completeness ($L$-completeness) of null hypersurfaces immersed in a Lorentzian manifold $M^{n+1}_1$, and show that $L$-complete null hypersurfaces are totally geodesic if $M^{n+1}_1$ satisfies the null energy condition (NEC). As a consequence, $L$-complete null hypersurfaces in a Lorentzian space form are totally geodesic.