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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Non-compact Einstein manifolds with symmetry
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by Christoph Böhm and Ramiro A. Lafuente
J. Amer. Math. Soc. 36 (2023), 591-651
DOI: https://doi.org/10.1090/jams/1022
Published electronically: February 28, 2023

Abstract:

For Einstein manifolds with negative scalar curvature admitting an isometric action of a Lie group $\mathsf {G}$ with compact, smooth orbit space, we show that the nilradical $\mathsf {N}$ of $\mathsf {G}$ acts polarly and that the $\mathsf {N}$-orbits can be extended to minimal Einstein submanifolds. As an application, we prove the Alekseevskii conjecture: Any homogeneous Einstein manifold with negative scalar curvature is diffeomorphic to a Euclidean space.
References
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Bibliographic Information
  • Christoph Böhm
  • Affiliation: University of Münster, Einsteinstraße 62, 48149 Münster, Germany
  • Email: cboehm@math.uni-muenster.de
  • Ramiro A. Lafuente
  • Affiliation: School of Mathematics and Physics, The University of Queensland, St. Lucia, QLD 4072, Australia
  • MR Author ID: 1011421
  • ORCID: 0000-0003-1719-1766
  • Email: r.lafuente@uq.edu.au
  • Received by editor(s): December 13, 2021
  • Published electronically: February 28, 2023
  • Additional Notes: The first-named author was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044 -390685587, Mathematics Münster: Dynamics-Geometry-Structure, and the Collaborative Research Centre CRC 1442, Geometry: Deformations and Rigidity. The second-named author is an Australian Research Council DECRA fellow (project ID DE190101063).
  • © Copyright 2023 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 36 (2023), 591-651
  • MSC (2020): Primary 53C25, 53C21, 53C30; Secondary 14L24
  • DOI: https://doi.org/10.1090/jams/1022
  • MathSciNet review: 4583772