This hyperbolic manifold is only partly compact. For more on this see Levin, Barrow, Bunn and Silk, Phys. There is a flat spot in the sky on this curved space. Down the narrow throat of the horn, the space is too small to fit fluctuations in temperature on the scales COBE can measure. So light emanating from that direction does not show hot and cold spots.
Fluctuations begin to appear in the direction of the wider parts of the horn.
3-D flat space can be made topologically compact by beginning with either a parallelepiped or a hexagonal prism as the finite fundamental domain. Six different orientable, compact spaces can be constructed by gluing oppsite faces of the fundamental polyhedron. Below we show the simulated COBE sky for a compact space built from a parallelepiped tiling with one of the faces twisted by 180 degrees before being affixed to its counterpart. We are currently developing ways to pull that pattern out of maps such as the one above to reveal the underlying geometry.