  Dark energy models due to a slowly evolving scalar (quintessence) field
$\phi$ are studied for various potentials $V(\phi)$ in a universe with negative
curvature. The potentials differ in whether they possess a minimum at $\phi=0$
or are monotonically declining, i.e. have a minimum at infinity. The angular
power spectrum $C_l$ of the cosmic microwave background (CMB) as well as the
magnitude-redshift relation $m_B(z)$ of the type Ia supernovae are compared
with the quintessence models. It is demonstrated that some of the models with
$\Omega_tot \simeq 0.85...0.9$ are in agreement with the observations, i.e.
possess acoustic peaks in the angular power spectrum of the CMB anisotropy as
observed experimentally, and yield a magnitude-redshift relation in agreement
with the data. Furthermore, it is found that the power spectrum $P(k)$ of the
large-scale structure (LSS) agrees with the observations too.
