Conformal screen on lightlike hypersurfaces.

Abstract

We study some properties of a lightlike hypersurface M , of a Lorentzian manifold, whose shape operator is conformal to the shape operator of its screen distribution. We prove that some specified aspects of the null geometry of M reduce to the Riemannian geometry of a leaf of its screen distri- bution. As a physical relevance, we show that there exists such a class of screen globally conformal lightlike hypersurfaces of 4-dimensional stationary non-flat spacetimes which admit a Killing horizon.