  In this paper, we give the Cartan's formula for half-lightlike submanifolds
of Lorentzian manifolds and use it to show that a screen homothetic
half-lightlike submanifolds of a Lorentzian space form, with a conformal
co-screen distribution are locally a lightlike triple product manifolds. Then
we give a classification theorem for half-lightlike submanifolds of Lorentzian
space form with constant screen principal curvatures. These results extend some
results obtained in the case of lightlike hypersurfaces of Lorentzian manifolds
([1]).
