  A classic result due to Furstenberg is the strict ergodicity of the horocycle
flow for a compact hyperbolic surface. Strict ergodicity is unique ergodicity
with respect to a measure of full support, and therefore implies minimality.
The horocycle flow has been previously studied on minimal foliations by
hyperbolic surfaces on closed manifolds, where it is known not to be minimal in
general. In this paper, we prove that for the special case of Riemannian
foliations, strict ergodicity of the horocycle flow still holds. This in
particular proves that this flow is minimal, which establishes a conjecture
proposed by Matsumoto.
  The main tool is a theorem due to Coud\`ene, which he presented as an
alternative proof for the surface case. It applies to two continuous flows
defining a measure-preserving action of the affine group of the line on a
compact metric space, precisely matching the foliated setting. In addition, we
briefly discuss the application of Coud\`ene's theorem to other kinds of
foliations.
