 Killing-Yano two-form

For a Killing-Yano two-form, ${\nabla }_a{Y}_{bc}$ is a differential three-form. Along a geodesic with velocity $v$, the covector $w_c=Y_{bc}{v}^b$ is carried by parallel transport, since $v^a{v}^b{\nabla }_a{Y}_{bc}=0$.