On Bochner Flat Kahler B-Manifolds

We obtain on a Kahler B-manifold (i.e., a Kahler manifold with a Norden metric) some corresponding results from the Kahlerian and para-Kahlerian context concerning the Bochner curvature. We prove that such a manifold is of constant totally real sectional curvatures if and only if it is a holomorphic Einstein, Bochner flat manifold. Moreover, we provide the necessary and sufficient conditions for a gradient Ricci soliton or a holomorphic ?-Einstein Kahler manifold with a Norden metric to be Bochner flat. Finally, we show that a Kahler B-manifold is of quasi-constant totally real sectional curvatures if and only if it is a holomorphic ?-Einstein, Bochner flat manifold.