  We modified the CLASS code in order to include relativistic galaxy number
counts in spatially curved geometries; we present the formalism and study the
effect of relativistic corrections on spatial curvature. The new version of the
code is now publicly available. Using a Fisher matrix analysis, we investigate
how measurements of the spatial curvature parameter $\Omega_K$ with future
galaxy surveys are affected by relativistic effects, which influence
observations of the large scale galaxy distribution. These effects include
contributions from cosmic magnification, Doppler terms and terms involving the
gravitational potential. As an application, we consider angle and redshift
dependent power spectra, which are especially well suited for model independent
cosmological constraints. We compute our results for a representative deep,
wide and spectroscopic survey, and our results show the impact of relativistic
corrections on the spatial curvature parameter estimation. We show that
constraints on the curvature parameter may be strongly biased if, in
particular, cosmic magnification is not included in the analysis. Other
relativistic effects turn out to be subdominant in the studied configuration.
We analyze how the shift in the estimated best-fit value for the curvature and
other cosmological parameters depends on the magnification bias parameter, and
find that significant biases are to be expected if this term is not properly
considered in the analysis.
