Nearly Kähler manifolds with vanishing Tricerri–Vanhecke Bochner curvature tensor

We study the local structures of nearly Kähler manifolds with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke (TV). We show that there does not exist a TV Bochner flat strict nearly Kähler manifold in 2n(⩾10)2n(⩾10) dimension and determine the local structures of the manifolds in 6 and 8 dimensions.