4-dimensional anti-Kähler manifolds
The notion of anti-Kähler manifold is used in the sense defined in the paper by \textit{A. Borowiec, M. Francaviglia} and \textit{I. Volovich} [Differ. Geom. Appl. 12, No. 3, 281--289 (2000; Zbl 0972.53043)]. Unfortunately, the Theorems 1 and 2 stating that a 4-dimensional anti-Kählerian manifold must be Einstein and locally symmetric are not true. For instance, the metric \(g=(dz^1)^2+f(z^1)(dz^2)^2\), \(f\) being an arbitrary non-constant holomorphic function, is not Einstein and not locally symmetric. The remaining results in fact are the same as those obtained in the above cited paper by A. Borowiec et al. (loc. cit.).
scientific article; zbMATH DE number 2133952