Einstein Kaehler submanifolds of a complex linear or hyperbolic space
The author proves that every Einstein Kaehler submanifold of \({\mathbb{C}}^ n\) or \({\mathbb{C}}H^ n\) (the complex hyperbolic space of negative constant holomorphic sectional curvature) is always totally geodesic. He uses in his proof some previous results (by himself) on the so-called ``diastasis'' associated to a metric, a notion introduced by \textit{E. Calabi} in Ann. Math., II. Ser. 58, 1-23 (1953; Zbl 0051.131)].
scientific article; zbMATH DE number 4058350
scientific article