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Einstein metrics on five-dimensional Seifert bundles

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Abstract

The aim of this article is to study Seifert bundle structures on simply connected 5-manifolds. We classify all such 5-manifolds which admit a positive Seifert bundle structure, and in a few cases all Seifert bundle structures are also classified. These results are then used to construct positive Ricci curvature Einstein metrics on these manifolds.

The proof has 4 main steps. First, the study of the Leray spectral sequence of the Seifert bundle, based on work of Orlik-Wagreich. Second, the study of log Del Pezzo surfaces. Third, the construction of Kähler-Einstein metrics on Del Pezzo orbifolds using the algebraic existence criterion of Demailly-Kollár. Fourth, the lifting of the Kähler-Einstein metric on the base of a Seifert bundle to an Einstein metric on the total space using the Kobayashi-Boyer-Galicki method.

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  1. Princeton University, 08544-1000, Princeton, NJ

    János Kollár

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  1. János Kollár
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Correspondence to János Kollár.

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Communicated by Steven Krantz

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Kollár, J. Einstein metrics on five-dimensional Seifert bundles. J Geom Anal 15, 445–476 (2005). https://doi.org/10.1007/BF02930981

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