Bochner and conformal flatness on normal complex contact metric manifolds (Q629923)

The authors prove that normal complex contact metric manifolds that are Bochner flat (the vanishing of the Bochner conformal tensor) must have constant holomorphic sectional curvature 4 and be Kähler. Moreover, if they are also complete and simply connected, this means that the manifolds are isometric to the odd-dimensional complex projective space \(\mathbb{C}P^{2n+1}(4)\) with the Fubini-Study metric. Finally, the authors prove that it is not possible for normal complex contact metric manifolds to be conformally flat.