we all know that we can get a riemannian metric by at least two method ,one is by the philosophy of the partition of the unit,while the other is by the whitney embedding theorem ,we can embed the riemannian manifold to an euclidean space of sufficiently large dimension,and we thus get a riemannian metric by the restriction of the canonical euclidean metri to the tangent vector bundle. Then what i want to ask is that whether all riemannian metrics can be constructed in the second way of above?