  Detailed account is given of the fact that the Cornell potential predicted by
Lattice QCD and its exactly solvable trigonometric extension recently reported
by us can be viewed as the respective approximate and exact counterparts on a
curved space to an 1/r flat space potential. The "curved" potential describes a
confinement phenomenon because it is of infinite depth and has only bound
states. It furthermore has the remarkable property of preserving both the SO(4)
and SO(2,1) symmetries of the ordinary 1/r potential. We first make the case
that this particular geometric version on confinement provides a remarkably
adequate description of both nucleon and Delta spectra and the proton mean
square charge radius as well, and suggests an intriguing venue toward quark
deconfinement as shut-down of the curvature considered as temperature
dependent. Next we observe that the SO(2,1) symmetry of the "curved" potential
allows to place it within the context of AdS_5/CFT correspondence and to
establish in this manner the algbraic link of the the latter to QCD
potentiology.
