  We investigate how the nature of dark energy affects the determination of the
curvature of the universe from recent observations. For this purpose, we
consider the constraints on the matter and dark energy density using
observations of type Ia supernovae, baryon acoustic oscillation peak and cosmic
microwave background with several types of dark energy equation of state.
Although it is usually said that the combination of current observations favors
a flat universe, we found that a relatively large parameter space allows the
universe to be open for a particular model of dark energy. We also discuss what
kind of dark energy model or prior allow a non-flat universe.
