Up to isometries, a deformation is a continuous function of its metric tensor
Philippe G. Ciarlet, Florian Laurent · Comptes Rendus Mathématique · 2002
If the Riemann–Christoffel tensor associated with a field of class 𝒞 2 of positive definite symmetric matrices of order three vanishes in a connected and simply connected open subset Ω ⊂ ℝ 3 , then this field is the metric tensor field associated with a deformation of class 𝒞 3 of the set Ω , uniquely determined up to isometries of ℝ 3 . We establish here that the mapping defined in this fashion is continuous, for ad hoc metrizable topologies.