A direct approach to quaternionic manifolds
  The recent definition of slice regular function of several quaternionic variables suggests a new notion of quaternionic manifold. We give the definition of quaternionic regular manifold, as a space locally modeled on $\mathbb{H}^n$, in a slice regular sense. We exhibit some significant classes of examples, including manifolds which carry a quaternionic affine structure. 
Graziano Gentili, Anna Gori, Giulia Sarfatti
math.CV