Generally we "draw" phase space as typical coordinate system, where $q$s and $p$s are treated like perpendicular axes. Why do we then regard phase space as generall differential manifold while it seems to be typical euclidean space? There is no curvature for example of phase space. I know that there is something special (symplecticity) about phase space, but it's not my question.
Why do we call phase space as differential manifold, while we don't consider curvature, only flat Euclidean space?