Abstract
Riemannian manifolds carrying skew (1, 1)-tensors satisfying the Killing-Yano equation are natural generalizations of nearly Kähler manifolds. In this article we investigate the existence of invariant solutions to the Killing-Yano equation on homogeneous spaces G/K endowed with a G-invariant metric, focusing on 2-forms. We exhibit non parallel invariant solutions on full flag manifolds SU(n) / T for every \(n \ge 4\). These flag manifolds do not admit an invariant nearly Kähler structure. We give the full set of invariant solutions to the Killing-Yano equation for SU(3) / T.
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Acknowledgements
We would like to thank M.L. Barberis for helpful conversations during the preparation of the manuscript. We also thank Ilka Agricola and Uwe Semmelman for very useful discussions.
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To Joseph Wolf, a great mentor of our geometry group in Córdoba.
The authors were partially supported by CONICET, ANPCyT and SECyT-UNC (Argentina).
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Dotti, I.G., Herrera, A.C. Killing-Yano 2-forms on homogeneous spaces. São Paulo J. Math. Sci. 12, 227–245 (2018). https://doi.org/10.1007/s40863-018-0101-4
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DOI: https://doi.org/10.1007/s40863-018-0101-4