Abstract
In this paper, we study the problem of the existence of left invariant Ricci flat metrics on nilpotent Lie groups. We mainly prove that any nilpotent Lie algebra obtained by a double extension of an Abelian Lie algebra admits at least one left invariant Ricci flat metric. As an application, we obtain certain new nilpotent Lie algebras which admit left invariant Ricci flat metrics.
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Acknowledgements
The authors wish to thank the reviewers for helpful comments.
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Funding was provided by the National Natural Science Foundation of China (Grant No. 11701300).
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Zaili Yan was supported by K.C. Wong Magna Fund in Ningbo University.
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Xiang, Y., Yan, Z. Existence of left invariant Ricci flat metrics on nilpotent Lie groups. Arch. Math. 117, 569–578 (2021). https://doi.org/10.1007/s00013-021-01645-6
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DOI: https://doi.org/10.1007/s00013-021-01645-6