Let (M,I,ω,Ω) be a nearly Kähler 6–manifold, that is, an SU(3)–manifold with
(3,0)–form Ω and Hermitian form ω which satisfies dω = 3λReΩ, dImΩ = −2λω2 for
a nonzero real constant λ. We develop an analogue of the Kähler relations on M,
proving several useful identities for various intrinsic Laplacians on M. When M is
compact, these identities give powerful results about cohomology of M. We show
that harmonic forms on M admit a Hodge decomposition, and prove that
Hp,q(M) = 0 unless p = q or (p = 1, q = 2) or (p = 2, q = 1).