A geometrical construction of a four-dimensional space-time from a torsion-free linear metric connection on a five-dimensional manifold M is described, based on a partially fixed reference cross-section of the bundle of frames of M. It is shown that the connection of M satisfies a generally invariant equation containing a fundamental length, while the space-time connection satisfies the Einstein vacuum equations. Dependence on the Schwarzschild solution on the choice of the reference cross-section of M is investigated. When the fundamental constant has the value of the Planck length and the chosen reference cross-section eliminates the spatial dimensions of the constructed observable space, the Schwarzschild solution leads to the rotation exp[itmc²/h], thus establishing a link between the classical and the quantum descriptions of a particle at rest.
Nuovo Cimento Della Societa Italiana Di Fisica B: General Physics Relativity Astronomy and Mathematical Physics and Methods Vol. 122, Issue 1, p. 75-87