Métriques riemanniennes holomorphes en petite dimension. (Holomorphic Riemannian metrics in small dimension) (Q5956584)

The paper deals with holomorphic Riemannian metrics on compact complex manifolds that are not necessarily Kähler. The author shows that a compact complex surface with a holomorphic Riemannian metric is a finite quotient of complex torus with flat metric. The main result of this paper is that there exists no such metric on any simply-connected complex \(3\)-fold.