  When minimal length uncertainty emerging from generalized uncertainty
principle (GUP) is thoughtfully implemented, it is of great interest to
consider its impacts on {\it "gravitational} Einstein field equations (gEFE)
and to try to find out whether consequential modifications in metric
manifesting properties of quantum geometry due to quantum gravity. GUP takes
into account the gravitational impacts on the noncommutation relations of
length (distance) and momentum operators or time and energy operators, etc. On
the other hand, gEFE relates {\it classical geometry or general relativity
gravity} to the energy-momentum tensors, i.e. proposing quantum equations of
state. Despite the technical difficulties, we confront GUP to the metric tensor
so that the line element and the geodesic equation in flat and curved space are
accordingly modified. The latter apparently encompasses acceleration, jerk, and
snap (jounce) of a particle in the {\it "quasi-quantized"} gravitational field.
Finite higher-orders of acceleration apparently manifest phenomena such as
accelerating expansion and transitions between different radii of curvature,
etc.
