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.
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Received 25 October 1996 / Revised version 1 April 1997
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Wang, J., Wang, M. Einstein metrics on \(S^{2}\)-bundles. Math Ann 310, 497–526 (1998). https://doi.org/10.1007/s002080050158
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DOI: https://doi.org/10.1007/s002080050158