Killing-Yano two-form
= Killing-Yano two-form
{c}
{title2=$Y_{ab}=-Y_{ba},\quad\nabla_{(a}Y_{b)c}=0$}
For a Killing-Yano two-form, $\nabla_aY_{bc}$ 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 $v^av^b\nabla_aY_{bc}=0$.