Rigidity of homogeneous Lamé systems

In this short paper, we show that any Lamé system whose Dirichlet-to-Neumann map for the elastic wave equation agrees with the one arising from the homogeneous Lamé system must actually be homogeneous. We do not need to impose any assumptions on the Lamé coefficients that we aim to recover. We use the fact that the homogeneous system gives rise to a geometry that is simple and admits a strictly convex foliation.