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January 2019 Einstein solvmanifolds have maximal symmetry
Carolyn S. Gordon, Michael R. Jablonski
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J. Differential Geom. 111(1): 1-38 (January 2019). DOI: 10.4310/jdg/1547607686

Abstract

All known examples of homogeneous Einstein metrics of negative Ricci curvature can be realized as left-invariant Riemannian metrics on solvable Lie groups. After defining a notion of maximal symmetry among left-invariant Riemannian metrics on a Lie group, we prove that any left-invariant Einstein metric of negative Ricci curvature on a solvable Lie group is maximally symmetric. This theorem is motivated both by the Alekseevskii Conjecture and by the question of stability of Einstein metrics under the Ricci flow. We also address questions of existence of maximally symmetric left-invariant Riemannian metrics more generally.

Funding Statement

The first author’s research was partially supported by National Science Foundation grant DMS-0906168.
The second author’s research was partially supported by National Science Foundation grant DMS-1612357 and a grant from the Simons Foundation (#360562, Michael Jablonski).

Citation

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Carolyn S. Gordon. Michael R. Jablonski. "Einstein solvmanifolds have maximal symmetry." J. Differential Geom. 111 (1) 1 - 38, January 2019. https://doi.org/10.4310/jdg/1547607686

Information

Received: 1 December 2015; Published: January 2019
First available in Project Euclid: 16 January 2019

zbMATH: 07004530
MathSciNet: MR3909903
Digital Object Identifier: 10.4310/jdg/1547607686

Rights: Copyright © 2019 Lehigh University

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Vol.111 • No. 1 • January 2019
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