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. Pope, N. Koiso, and Y. Sakane. Corresponding new Einstein-Weyl structures are also constructed.