A NOTE ON THE GOLDBERG CONJECTURE OF WALKER MANIFOLDS

This paper is concerned with Goldberg conjecture. Using the phi(phi)-operator we prove the following result. Let (M, phi, (w)g) be an almost Kahler-Walker-Einstein compact manifold with the proper almost complex structure.. The proper almost complex structure. on Walker manifold (M, (w)g) is integrable if phi(phi)g(N+) = 0, where g(N+) is the induced Norden-Walker metric on M. This resolves a conjecture of Goldberg under the additional restriction on Norden-Walker metric (g(N+) is an element of Ker phi(phi)).