A quantum representation of the homogeneous 5D manifold and the Perelman mappings of 5D onto non-homogeneous Lorentz 4D manifolds

Abstract

The expression of the Maxwell magnetic monopole was employed to correlate the space to space projection that gives rise to the Gell-Mann standard model, and space to time projection which gives the leptons; and how does it correlate to the Perelman mappings from the homogeneous 5D manifold to the Lorentz 4D manifold, together with correlating the physical consequences caused by the breaking of the Diagonal Long Range Order [DLRO] of the monopoles quantum states affected by the motion of massive particles in the Lorentz 4D boundary of the 5D manifold, which leads to gravitons and the gravity field via the General Relativity covariant Riemannian 4D curvatures metric equation.