Bochner and conformal flatness on normal complex contact metric manifolds.

We will prove that normal complex contact metric manifolds that are Bochner flat must have constant holomorphic sectional curvature 4 and be Kähler. If they are also complete and simply connected, they must be isometric to the odd-dimensional complex projective space $${{\mathbb{C}P^{2n+1}}}$$(4) with the Fubini-Study metric. On the other hand, it is not possible for normal complex contact metric manifolds to be conformally flat. [ABSTRACT FROM AUTHOR]