  We compute exact thermodynamic geometric properties of the non-abelian
quarkonium bound states from the consideration of one-loop strong coupling.
From the general statistical principle, the intrinsic geometric nature of
strongly coupled QCD is analyzed for the Columbic, rising and Regge rotating
regimes. Without any approximation, we have obtained the non-linear mass effect
for the Bloch-Nordsieck rotating strongly coupled quarkonia. For a range of
physical parameters, we show in each cases that there exists a well-defined,
non-degenerate, curved, intrinsic Riemannian manifold. As the gluons become
softer and softer, we find in the limit of the Bloch-Nordsieck resummation that
the strong coupling obtained from the Sudhakov form factor possesses exact
local and global thermodynamic properties of the underlying mesons, kaons and
$D_s$ particles.
