Some structural features induced by the space-time metrical fluctuation in the theory of gravitational fields

Under the assumption that the so-called space-time fluctuation y(x) in a classical sense, attached to each point of the gravitational field at some microscopic stage, is summarized as the metrical fluctuation in the form g/sub lambdakappa/(x) = g/sub lambdakappa/(x) x exp 2sigma(y(x)), some new physical aspects induced by the conformal scalar sigma(x) (equivalent sigma(y(x))) are found: By introducing the torsion T-bar/sup kappa//sub lambdamu/(x) from a general standpoint, the resulting micro-gravitational field is made to have a conformally non-Riemannian structure, where a special form of T-bar/sup kappa//sub lambdamu/ (i.e., T-bar/sup kappa//sub lambdamu/ = delta/sup kappa//sub lambda/sigma/sub μ/-delta/sup kappa//sub μ/sigma/sub lambda/(sigma/sub μ/ = partialsigma/partialx/sup μ/)) shows some peculiar features. An averaging process with respect to y is taken into account, by which the spatial structure of the corresponding macro-field is shown, in general, to have a somewhat ''non''-Riemannian structure due to the contributions of the torsion T-bar/sup kappa//sub lambdamu/