Conformal Killing 2-forms on four-dimensional manifolds
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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.
KeywordsConformal Killing forms Invariant conformally Kähler structures Half-conformally flat metrics
Mathematics Subject Classification53C25 53C15 53C30
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