Hypercomplex structures on Courant algebroids

Abstract Hypercomplex structures on Courant algebroids unify holomorphic symplectic structures and usual hypercomplex structures. In this Note, we prove the equivalence of two characterizations of hypercomplex structures on Courant algebroids, one in terms of Nijenhuis concomitants and the other in terms of (almost) torsionfree connections for which each of the three complex structures is parallel. To cite this article: M. Stienon, C. R. Acad. Sci. Paris, Ser. I 347 (2009).