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.
