  The higher dimensional Quantum General Relativity of a Riemannian manifold
being an embedded space in a space-time being a Lorentzian manifold is
investigated. The model of quantum geometrodynamics, based on the
Wheeler-DeWitt equation reduced to a first order functional quantum evolution
supplemented through an additional eigenequation for the scalar curvature, is
formulated. Furthermore, making use of the objective quantum gravity and global
one-dimensional conjecture, the general wave function beyond the Feynman path
integral technique is derived. The resulting quantum gravity model creates the
opportunity of potentially new theoretical and phenomenological applications
for astrophysics, cosmology, and physics.
