Abstract
We study four-dimensional simply connected Lie groups G with a left invariant Riemannian metric g admitting non-trivial conformal Killing 2-forms. We show that either the real line defined by such a form is invariant under the group action, or the metric is half-conformally flat. In the first case, the problem reduces to the study of invariant conformally Kähler structures, whereas in the second case, the Lie algebra of G belongs (up to homothety) to a finite list of families of metric Lie algebras.
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The first and second authors were partially supported by CONICET, ANPCyT and SECyT-UNC (Argentina), and the third author was partially supported by the ANR-10-BLAN 0105 grant of the Agence Nationale de la Recherche (France).
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Andrada, A., Barberis, M.L. & Moroianu, A. Conformal Killing 2-forms on four-dimensional manifolds. Ann Glob Anal Geom 50, 381–394 (2016). https://doi.org/10.1007/s10455-016-9517-1
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DOI: https://doi.org/10.1007/s10455-016-9517-1