Half-Lightlike Submanifold of a Lorentzian Manifolds with a Conformal Co-screen Distribution

Abstract

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 submanifold of a Lorentzian space form, with a closed conformal co-screen distribution is locally a lightlike triple product manifold. Then we give a classification theorem for half-lightlike submanifolds of Lorentzian space form with constant screen principal curvatures. These results extend some ones obtained in the case of lightlike hypersurfaces of Lorentzian manifolds.