Hypercomplex Structures on Courant Algebroids
نویسنده
چکیده
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. A Courant algebroid [4] consists of a vector bundle π : E → M , a nondegenerate symmetric pairing 〈, 〉 on the fibers of π, a bundle map ρ : E → TM called anchor and an R-bilinear operation ◦ on Γ(E) called Dorfman bracket, which, for all f ∈ C(M) and x, y, z ∈ Γ(E) satisfy the relations x ◦ (y ◦ z) = (x ◦ y) ◦ z + y ◦ (x ◦ z); (1) ρ(x ◦ y) = [ρ(x), ρ(y)]; (2) x ◦ fy = (
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