Abstract
This is the English translation of "Metriques Kahleriennes et Fibres Holomorphes" written by E. Calabi. The systematic way to construct the kahler metrics on the holomorphic bundles over the compact kahler manifolds or on their open sets which satisfy the certain axioms are studied. The section 4 and the section 5 are devoted to Einstein-kahler metrics on the line bundles over Einstein-kahler manifolds and to hyperkahler metrics, respectively. Many explicit examples such as the complete Ricci-flat kahler metrics on the canonical bundles of Einstein-kahler manifolds and the hyperkahler metrics on the cotangent bundles of the Fubini-Study spaces are included.
