  This is a continuation of our previous work (Advances in Mathematics 450
(2024), Paper No. 109768). In this paper, we characterize complete metrics with
finite total Q-curvature as normal metrics for all dimensional cases. Secondly,
we introduce another volume entropy to provide geometric information regarding
complete non-normal metrics with finite total Q-curvature. In particular, we
show that if the scalar curvature is bounded from below, the volume growth of
such complete metrics is controlled.
