The Cosmic Microwave Background ( CMB ) anisotropy constrains the geometry of the Universe because the positions of the acoustic peaks of the angular power spectrum depend strongly on the curvature of underlying three-dimensional space .
In this Letter we exploit current observations to determine the spatial geometry of the Universe in the presence of isocurvature modes .
Previous analyses have always assumed that the cosmological perturbations were initially adiabatic . A priori one might expect that allowing additional isocurvature modes would substantially degrade the constraints on the curvature of the Universe .
We find , however , that if one considers additional data sets , the geometry remains well constrained .
When the most general isocurvature perturbation is allowed , the CMB alone can only poorly constrain the geometry to \Omega _ { 0 } = 1.6 \pm 0.3 .
Including large-scale structure ( LSS ) data one obtains \Omega _ { 0 } = 1.07 \pm 0.03 , and \Omega _ { 0 } = 1.06 \pm 0.02 when supplemented by the Hubble Space Telescope ( HST ) Key Project determination of H _ { 0 } and SNIa data .