Einstein metrics on $$S^{2}$$-bundles

Abstract. New Einstein metrics are constructed on the associated $${\Bbb R}{\Bbb P}^2$$, $$S^2$$, and $${\Bbb R}^2$$-bundles of principal circle bundles with base a product of Kähler-Einstein manifolds with positive first Chern class and with Euler class a rational linear combination of the first Chern classes. These Einstein metrics represent different generalizations of the well-known Einstein metrics found by Bérard Bergery, D. Page, C. …