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Spaces equipped with two complementary (distinct) congruences of self-dualnull strings and at least one congruence of anti-self-dual null strings areconsidered. It is shown that if such spaces are Einsteinian then the vacuumEinstein field equations can be reduced to a single nonlinear partialdifferential equation of the second order. Different forms of these equationsare analyzed. Finally, several new explicit metrics of the para-Hermite andpara-K\"{a}hler Einstein spaces with $\Lambda \ne 0$ are presented. Somerelation of that metrics to a modern approach to mechanical issues isdiscussed.

On some examples of para-Hermite and para-K\"{a}hler Einstein spaces with $\Lambda \ne 0$