Sur les metriques admettant les plans comme surfaces minimales

We establish the system of partial differential equations satisfied by the riemannian metrics on open subsets of ${\mathbb {R}}^{3}$ which admit planes as minimal surfaces. This is a nonlinear system of 10 partial differential equations, with the euclidian metric as a particular solution. In a previous work, we solved this system for axially symmetrical metrics. In this paper we linearize the system at the euclidian metric and solve the linear system. We obtain a 20-dimensional space of solutions.