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
- 6.De Smedt, V., Salamon, S.: Anti-self-dual metrics on Lie groups. Differential geometry and integrable systems (Tokyo, 2000). Contemporary Mathematics, vol. 308, pp. 63–75. American Mathematical Society, Providence, RI (2002)Google Scholar
- 7.Gauduchon, P., Moroianu, A.: Killing 2-forms in dimension 4, arXiv:1506.04292