The conformal geometry of sub manifolds spaces and their some applications to kinematic quantities of space times

The aims of this study is to identify the conformal geometry of submanifold in a Riemannian spaces and a related some problems We followed the historical , analysis mathematical method and we found that : any Riemannian manifold is a Riemannian metric also every Riemannian 2-manifolds are conformally flat, Since for any semi Riemannian manifold, there is a natural existence of a light like subspace (hypersurface or submanifold),whose metric is degenerate, one fails to use the theory of harmonic maps of non-degenerate manifolds for the light like case  and there are many physical applications of manifolds.