Background
In my general relativity class the lecturer gave us three set of line elements:
$$ ds^2 = dx^2 + dy^2 $$
$$ ds^2 = dx'^2 + x'^2 dy'^2 $$
$$ ds^2 = dA^2 + \sin^2 (A) dB^2$$
And (later) told us the first two were related by coordinated transformations (Cartesian and polar co-ordinates). The third one describes a different geometry and thus cannot be related by a coordinate transformation. He then said it was an open problem for number of dimensions greater than $4$ regrading if two arbitrary line-elements could be changed into another by a coordinate transformation
Questions
What is the name of this open problem? How is it solved in $4$ dimensions or less?