Holonomy of the Obata connection on Joyce hypercomplex manifolds

In this talk, I will present a counterexample to this conjecture in quaternionic dimension 3. This example motivated a broader investigation, and we were able to prove that, except for a specific family of Joyce manifolds and the Hopf surface (which is Obata-flat), the Obata holonomy of any Joyce hypercomplex manifold is reducible.