A simple example of type-[N] circle times [N] HH-spaces admitting twisting null geodesic congruence

摘要

Expanding HH-spaces with cosmological constant of the type [deg] circle times [deg] are considered. We find the expanding hyperheavenly equation describing such spaces and then we specify this equation to the case of the type [N] circle times [N]. An example of the solution of this last equation leading to the type-[N] circle times [N] HH-space (with vanishing cosmological constant) admitting twisting null geodesic congruence is presented and the respective metric is explicitly given.