Gravity: Is there curved space besides curved spacetime? Wikipedia:

Curved spaces play an essential role in General Relativity where
  gravity is often visualized as curved space.

Is the Wikipedia article "curved space" talking about curved space or about curved spacetime? As far as I know gravity is curving spacetime, not space.
I tried here a little proof of the possibility to reduce any curved space to flat space (for simplification I consider 2D space instead of 3D space, but it might also work for 3D space):
Lets start with an isolated group of mass objects. Gravitation acts all over the universe, but we consider only a zone on the border of which curvature is infinitesimally small because of the absence of mass near the border. We represent this zone by a sort of stamped plastic sheet (the blue sheet), and we place it upon the green flat sheet of paper. 

Supposing that there is no curvature with an angle of 90° or more, we can assign to each point of the green sheet one point on the blue sheet, so that we get flat coordinates.
Question: Should the title of the Wikipedia article be "Curved spacetime" instead of "Curved space"?
 A: Your argument is incorrect: The curvature of a spatial slice is coordinate-independent.
What is true is that in general relativity, there is a priori no preferred spatial slicing. For example, de Sitter spacetime (a universe dominated by cosmological constant) can be sliced into positively curved, negatively curved or flat spaces.
When we say that our universe appears to be spatially flat, we're talking about a particular slicing selected by the matter distribution, which we believe does come in layers of constant cosmological time.
A: You ask the question of whether the title for the Wikipedia article should be "Curved Spacetime" instead of "Curved Space".
The answer is a resounding no, leave it as is. The article itself covers strictly the mathematics of any curved space and is not specific to physics contexts. As is, the usage of "Space" does not mean purely spatial and not temporal dimensions as it does in physics. Furthermore, from the definition given, it is clear that even in a physics context, they are referring to principally spatial curvature in a metric.
It is curious that they wouldn't call this article "Intrinsic Curvature", however as I am not a mathematician, I won't comment on their choices.
But the fact is that there is no inclusion of time and that this is more a treatise of the mathematics, for which the label "Curved Space" is very much appropriate. So no, the title should not be changed.
