Quote by PAllen
And I ask you again to think about my simple embedding example. The surface of a globe is noneuclidean. The globe is sitting in a flat euclidean 3space. Contradiction? No. The embedded space is curved, the space embedded in happens to be flat.

No problem in agreeing with that situation.
Also recall my discussion with Peter: the SC geometry allows embedding of completely flat 3space regions. The K factor is actually a feature of a particular class of observers (static observers, which are noninertial observers), not something intrinsic to the geometry. It is analogous to distortions seen in an accelerating rocket in flat spacetime  a feature of the observer, not the intrinsic spacetime geometry. GP observers in the same SC geometry, experience absolutely flat 3space.

In that more generaized context I see the point, no problems.