There are classical results showing that if a negatively closed manifold has its horospheres of constant mean curvature then it is locally symmetric. Here we shall present a rigidity result involving the intrinsic Riemannian structure of these horospheres. More precisely if one of them is flat than the closed manifold is locally real hyperbolic. Several questions arose from the approach that we will discuss, in particular concerning replacing the hypothesis on the curvature by the assumption that there is no conjugate points. This is based on a joint work with G. Courtois and S. Hersonsky.