Light-like Hypersurfaces of Meta-Metallic Semi-Riemannian Manifolds and Its Application to the Universe Expansion

Abstract

In this study, we introduce light-like hypersurfaces of a meta-metallic semi-Riemannian manifold via the meta-metallic-Chi ratio. We get characterizations of induced structures on a light-like hypersurface with the help of the meta-metallic semi-Riemannian structure. Particularly, we introduce some subclasses of light-like hypersurfaces such as invariant, anti-invariant and screen semi-invariant light-like hypersurfaces of meta-metallic semi-Riemannian manifolds. We give a non-existence theorem about radical anti-invariant light-like hypersurface of meta-metallic semi-Riemannian manifold. Especially, we obtain geometric characterizations of distributions of screen semi-invariant light-like hypersurfaces of a meta-metallic semi-Riemannian manifold. Additionally, in this paper, an example of an invariant light-like hypersurface is given using the De Sitter metric, which is used in the expansion of the universe.