Compact conformally Kähler Einstein-Weyl manifolds (Q1941071)

The author proves that a compact Einstein-Weyl manifold \(M\) with Hermitian Ricci tensor admits a holomorphic Killing vector field and consequently, \(M\) is a complex projective space \(\mathbb{CP}^n\) or \(M=\mathbb{P}(L\oplus \mathcal{O})\) where \(L\) is a holomorphic line bundle over a Kähler-Einstein manifold with positive scalar curvature.