Application of the L2-orthogonal decomposition of the second fundamental form of the hypersurfaces and the Ahlfors Laplacian to the study of the general relativistic vacuum constraint equations

In this paper, we consider a [Formula: see text]-orthogonal decomposition of the second fundamental form of a closed spacelike hypersurface in a Lorentzian spacetime and its applications to the study of some algebraic-differential properties of the general relativistic vacuum constraint equations. For the study, we will use the well-known Ahlfors Laplacian.