I've heard once assertions of the sort:
- Let there isbe a Riemann metric (not very smooth, say of a class $C^1$ or $C^2$ or may bemaybe $C$?) in a neibourhoodneighbourhood of a point on a manifold. Then it is possible to choose such coordinates whatso that the metric is $C^\infty$ or even analiticanalytic in them.
- In case of 3-dimentionaldimensional manifolds it is possible to choose such coordinates globally, so the manuifoldmanifold becomes a smooth one. In the case of higher dimentionsdimensions $n\ge4$ it is not true.
Are those assertions true? I've heard them some time ago and not sure I remember all the details. Is it a well-known thing? Are there some detailed references?