Abstract
We study left invariant conformal Killing–Yano (CKY) 2-forms on Lie groups endowed with a left invariant metric. We classify all 5-dimensional metric Lie algebras carrying CKY tensors that are obtained as a one-dimensional central extension of 4-dimensional metric Lie algebras endowed with an invertible parallel skew-symmetric tensor. On the other hand, we also classify 5-dimensional metric Lie algebras with center of dimension greater than one admitting strict CKY tensors. In addition, we determine all possible CKY tensors on these metric Lie algebras. In particular, we exhibit the first examples of CKY 2-forms on metric Lie algebras which do not admit any Sasakian structure.
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Acknowledgements
Part of this work has been set up during the visit of the first-named author at KU Leuven, she thanks the Mathematics department at Campus Kulak Kortrijk for their hospitality. The authors would like to thank Adrián Andrada for several interesting discussions on the subject, and we are also grateful to the anonymous referee for carefully reading the manuscript and her/his suggestions that improved the exposition of the paper.
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The authors were partially supported by CONICET, ANPCyT and SECyT-UNC (Argentina). The second author was also supported by the Research Foundation - Flanders (FWO Project G.0F93.17N) and ARC (Australia) DP190100317.
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Herrera, A., Origlia, M. Invariant Conformal Killing–Yano 2-Forms on Five-Dimensional Lie Groups. J Geom Anal 32, 210 (2022). https://doi.org/10.1007/s12220-022-00951-x
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DOI: https://doi.org/10.1007/s12220-022-00951-x