Invariant solutions to the conformal Killing–Yano equation on Lie groups

We search for invariant solutions of the conformal Killing–Yano equation on Lie groups equipped with left invariant Riemannian metrics, focusing on 2-forms. We show that when the Lie group is compact equipped with a bi-invariant metric or 2-step nilpotent, the only invariant solutions occur on the 3...

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Bibliographic Details
Published in:Journal of geometry and physics 2015-08, Vol.94, p.199-208
Main Authors: Andrada, A., Barberis, M.L., Dotti, I.G.
Format: Article
Language:English
Subjects:
Conformal Killing–Yano 2-forms
Left invariant metrics
Lie groups
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Summary:We search for invariant solutions of the conformal Killing–Yano equation on Lie groups equipped with left invariant Riemannian metrics, focusing on 2-forms. We show that when the Lie group is compact equipped with a bi-invariant metric or 2-step nilpotent, the only invariant solutions occur on the 3-dimensional sphere or on a Heisenberg group. We classify the 3-dimensional Lie groups with left invariant metrics carrying invariant conformal Killing–Yano 2-forms.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2015.04.004