  Constraining simultaneously the Dark Energy(DE) equation of state and the
curvature of the Universe is difficult due to strong degeneracies. To
circumvent this problem when analyzing data it is usual to assume flatness to
constrain DE, or conversely, to assume that DE is a cosmological constant to
constrain curvature. In this paper, we quantify the impact of such assumptions
in view of future large surveys. We simulate future data for type Ia Supernovae
(SNIa), Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations
(BAO) for a large range of fiducial cosmologies allowing a small spatial
curvature. We take into account a possible time evolution of DE through a
parameterized equation of state : $w(a) = w_0 + (1-a) w_a$. We then fit the
simulated data with a wrong assumption on the curvature or on the DE
parameters. For a fiducial $\Lambda$CDM cosmology, if flatness is incorrectly
assumed in the fit and if the true curvature is within the ranges
$0.01<\Omega_k<0.03$ and $-0.07<\Omega_k<-0.01$, one will conclude erroneously
to the presence of an evolving DE, even with high statistics. On the other
hand, models with curvature and dynamical DE can be confused with a flat
$\Lambda$CDM model when the fit ignores a possible DE evolution. We find that,
in the future, with high statistics, such risks of confusion should be limited,
but they are still possible, and biases on the cosmological parameters might be
important. We conclude on recalling that, in the future, it will be mandatory
to perform some complete multi-probes analyses, leaving the DE parameters as
well as the curvature as free parameters.
