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New pseudo Einstein metrics on Einstein solvmanifolds

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Abstract

A Riemannian Einstein manifold is called an Einstein solvmanifold if there exists a transitive solvable group of isometries. In this short note, we show that every Einstein solvmanifold admits at least one pseudo-Riemannian Einstein metric.

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, P.R. China

    Hui Zhang

  2. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, Zhejiang, People’s Republic of China

    Zaili Yan

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  1. Hui Zhang
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  2. Zaili Yan
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Correspondence to Zaili Yan.

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This work is supported by NSFC (Nos. 11701300, 11626134) and K.C. Wong Magna Fund in Ningbo University.

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Zhang, H., Yan, Z. New pseudo Einstein metrics on Einstein solvmanifolds. manuscripta math. 166, 427–436 (2021). https://doi.org/10.1007/s00229-020-01249-4

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  • DOI: https://doi.org/10.1007/s00229-020-01249-4

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