Killing Symmetries in $\mathcal{H}$-Spaces with $Λ$

All Killing symmetries in complex $\mathcal{H}$-spaces with $Λ$ in terms of the Plebański - Robinson - Finley coordinate system are found. All $\mathcal{H}$-metrics with $Λ$ admitting a null Killing vector are explicitly given. It is shown that the problem of non-null Killing vector reduces to looking for solution of the Boyer - Finley - Plebański (Toda field) equation

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