Lightlike hypersurfaces on manifolds endowed with a conformal structure of Lorentzian signature

Abstract

The authors study the geometry of lightlike hypersurfaces on manifolds $(M, c)$ endowed with a pseudoconformal structure $c = CO (n - 1, 1)$ of Lorentzian signature. Such hypersurfaces are of interest in general relativity since they can be models of different types of physical horizons. On a lightlike hypersurface, the authors consider the fibration of isotropic geodesics and investigate their singular points and singular submanifolds. They construct a conformally invariant normalization of a lightlike hypersurface intrinsically connected with its geometry and investigate affine connections induced by this normalization. The authors also consider special classes of lightlike hypersurfaces. In particular, they investigate lightlike hypersurfaces for which the elements of the constructed normalization are integrable.