  The properties of the Tremblay-Turbiner-Winternitz system (related to the
harmonic oscillator) were recently studied on the two-dimensional spherical
$S_{\kappa}^2$ ($\kappa>0$) and hiperbolic $H_{\kappa}^2$ ($\kappa<0$) spaces
(J. Phys. A : Math. Theor. 47, 165203, 2014). In particular, it was proved the
higher-order superintegrability of the TTW system by making use of (i) a
curvature-dependent formalism, and (ii) existence of a complex factorization
for the additional constant of motion. Now a similar study is presented for the
Post-Winternitz system (related to the Kepler problem). The curvature $\kappa$
is considered as a parameter and all the results are formulated in explicit
dependence of $\kappa$. This technique leads to a correct definition of the
Post-Winternitz (PW) system on spaces with curvature $\kappa$, to a proof of
the existence of higher-order superintegrability (in both cases, $\kappa>0$ and
$\kappa<0$), and to the explicit expression of the constants of motion.
