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Homogeneous Einstein
metrics on Euclidean spaces are Einstein solvmanifolds
Christoph Böhm and Ramiro A Lafuente |
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Geometry & Topology 26 (2022) 899–936
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Abstract |
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We show that homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, using the fact that they admit periodic, integrally minimal foliations by homogeneous hypersurfaces. For the geometric flow induced by the orbit–Einstein condition, we construct a Lyapunov function based on curvature estimates which come from real GIT. |
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Keywords
Einstein manifolds, homogeneous spaces, cohomogeneity-one
manifold
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Mathematical Subject Classification
Primary: 53C25, 53C30
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References |
Publication
Received: 13 December 2020
Accepted: 6 April 2021
Published: 15 June 2022
Proposed: John Lott
Seconded: Tobias H Colding, Bruce Kleiner
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Authors |
| Christoph Böhm | |
| Mathematisches Institut University of Münster Münster Germany |
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| Ramiro A Lafuente | |
| School of Mathematics and
Physics The University of Queensland, St Lucia campus Brisbane Australia |
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