Killing-Yano 2-forms on homogeneous spaces

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≥ 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.