I'm not quite sure what you mean by the term "model" in this context, but:

If a space is a Euclidean space, in the sense that it has a Euclidean metric, then its Levi Civita connection (the connection compatible with its metric) has no intrinsic curvature (for example a flat plane is like this). However, it may be given some extrinsic curvature by means of an embedding into a higher dimensional space (the flat plane may be rolled up into a cylinder in $\mathbb{R}^3$).

But if you were a two dimensional organism living on the cylinder, you couldn't detect this extrinsic curvature by locally measuring angles and distances.

This post imported from StackExchange Physics at 2014-03-22 16:54 (UCT), posted by SE-user twistor59