On rigid displacements and their relation to the infinitesimal rigid displacement lemma in shell theory

International audienceLet ω be an open connected subset of R^2 and let θ be an immersion from ω into R^3. It is established that the set formed by all rigid displacements of the surface θ(ω) is a submanifold of dimension 6 and of class C^∞ of the space H^1(ω). It is shown that the infinitesimal rigid displacements of the same surface θ(ω) span the tangent space at the origin to this submanifold