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"?