- #126

bapowell

Science Advisor

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It has positive and negative principle curvatures, but the Gaussian curvature is zero.Are you sure that the torus does not cumulate positive and negative curvatures?

They are not -- they are positively curved everywhere.n-spheres are locally flat as well

Right, but none of your criteria are strictly required by observations. We have no data supporting the size (finite vs. infinite) of the universe, whether it is globally compact or bounded, or whether it is globally homogeneous. What we know from observations of the observable universe is that it is approximately homogeneous and close to flat locally. Empirically, all three manifolds of constant curvature -- Euclidean (including toroidal and other flat geometries), spherical, and hyperbolic spaces -- are equally in the running.it is simply making the effort to not introduce hypotheses that are not strictly riquired by new observations.

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