  This is a corrected and essentially extended version of the previous preprint
arXiv:gr-qc/0105088 v4 (2002) by Y. Nutku and M. Sheftel containing new
results. It is being published now in honor of Y. Nutku's memory. All
responsibility for the additions and changes must be attributed to M. Sheftel.
We present new anti-self-dual exact solutions of the Einstein field equations
with Euclidean and neutral (ultra-hyperbolic) signatures that admit only one
rotational Killing vector. Such solutions of the Einstein field equations are
determined by non-invariant solutions of Boyer-Finley ($BF$) equation. For the
case of Euclidean signature such a solution of the $BF$ equation was first
constructed by Calderbank and Tod. Two years later, Martina, Sheftel and
Winternitz applied the method of group foliation to the Boyer-Finley equation
and reproduced the Calderbank-Tod solution together with new solutions for the
neutral signature. In the case of Euclidean signature we obtain new metrics
which asymptotically locally look like a flat space and have a non-removable
singular point at the origin. In the case of ultra-hyperbolic signature there
exist three inequivalent forms of metric. Only one of these can be obtained by
analytic continuation from the Calderbank-Tod solution whereas the other two
are new.
