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Extended graph 4-manifolds, and Einstein metrics

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Abstract

We show that extended graph 4-manifolds (as defined by Frigerio–Lafont–Sisto in [12]) do not support Einstein metrics.

Résumé

Nous montrons que les variétés grapheés généralisées de dimension 4 (définies par Frigerio–Lafont–Sisto dans [12]) n’admettent aucune métrique d’Einstein.

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Acknowledgements

The author would like to thank Professor Claude LeBrun for useful comments on an earlier version of this manuscript, and for generously sharing his knowledge of the subject over the years.

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  1. University of Florida, Gainesville, USA

    Luca F. Di Cerbo

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  1. Luca F. Di Cerbo
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Correspondence to Luca F. Di Cerbo.

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Supported in part by NSF Grant DMS-2104662.

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Di Cerbo, L.F. Extended graph 4-manifolds, and Einstein metrics. Ann. Math. Québec 48, 269–276 (2024). https://doi.org/10.1007/s40316-021-00192-4

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