Decomposition of the space of covariant two-tensors on R3

We show that the decomposition of the space of covariant two-tensors onR ³ is true in weighted Hölderian spaces, as in weighted Sobolev spaces, in the general case, that is without supposing the metric near the flat metric. M. Cantor proved, first, that a splitting of two-covariant tensor fields onR ⁿ in weighted Sobolev spaces was true. We apply this result to solve the problem of constraints, in general relativity; we show that this problem admits a solution in the most general case.