  The intrinsic geometric degree of freedom that was proposed to determine the
optimal correlation energy of the fractional quantum Hall states, is analyzed
for quantum confined planar electron systems. One major advantage in this case
is that the role of various unimodular metrics resulting from the absence of
rotational symmetry can be investigated independently or concurrently. For
interacting electrons in our system, the confinement metric due to the
anisotropy shifts the minimum of the ground state and the low-lying excited
states from the isotropic case much more strongly than the corresponding shift
due to the unimodular Galilean metric. Implications of these results for
possible observation of higher Landau level filling fractions have been
elucidated.
