= Square of a Killing-Yano two-form
{title2=$K_{ab}=Y_{ac}Y_b{}^c$}
The square is a <rank-two Killing tensor>. It is symmetric because it pairs the covectors $Y_{a\cdot}$ and $Y_{b\cdot}$ using the metric. Along every affinely parametrized <geodesic>, its contraction $K(v,v)$ is the squared norm of the carried by <parallel transport> covector $Y(v,\cdot)$. <Metric compatibility> makes that norm constant, proving the <Killing tensor> equation. On a <Riemannian manifold> this tensor is positive semidefinite.
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