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Anton Petrunin
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George Lowther
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I've heard once assertions of the sort:

  1. 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.
  2. 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?

I've heard once assertions of the sort:

  1. Let there is a Riemann metric (not very smooth, say of a class $C^1$ or $C^2$ or may be $C$?) in a neibourhood of a point on a manifold. Then it is possible to choose such coordinates what the metric is $C^\infty$ or even analitic in them.
  2. In case of 3-dimentional manifolds it is possible to choose such coordinates globally, so the manuifold becomes a smooth one. In case of higher dimentions $n\ge4$ 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?

I've heard assertions of the sort:

  1. Let there be a Riemann metric (not very smooth, say of class $C^1$ or $C^2$ or maybe $C$?) in a neighbourhood of a point on a manifold. Then it is possible to choose coordinates so that the metric is $C^\infty$ or even analytic in them.
  2. In case of 3-dimensional manifolds it is possible to choose such coordinates globally, so the manifold becomes a smooth one. In the case of higher dimensions $n\ge4$ 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?

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Andrew
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Questions on smoothness of Riemann metrics

I've heard once assertions of the sort:

  1. Let there is a Riemann metric (not very smooth, say of a class $C^1$ or $C^2$ or may be $C$?) in a neibourhood of a point on a manifold. Then it is possible to choose such coordinates what the metric is $C^\infty$ or even analitic in them.
  2. In case of 3-dimentional manifolds it is possible to choose such coordinates globally, so the manuifold becomes a smooth one. In case of higher dimentions $n\ge4$ 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?