Similarity Manifolds after Mickaël Kourganoff
A similarity structure on a manifold consists in giving a Riemannian metric on a neighborhood of each point such that the metrics on the intersection of two neighborhoods are homothetic, i.e. proportional by means of a locally constant function. The basic example is that of the cone over a Riemannian manifold which gives in the case of the standard sphere a (flat) Hopf manifold. The question is whether there exist more complicated examples?