  We investigate observational constraints on the curvature of the universe not
restricting ourselves to a cosmological constant as dark energy, in particular
allowing a dark energy equation of state to evolve with time in several ways.
We use type Ia supernovae (SNeIa) data from the latest gold data set which
includes 182 SNeIa, along with the CMB shift parameter and the baryon acoustic
oscillation peak. We show quantitatively that the constraint on the curvature
of the universe depends on dark energy model: some popular parametrizations
give constraints closely around the flat universe at 5% level (2 sigma C.L.)
whereas some parametrizations allow the universe to be as open as Omega_k ~
0.2.
