Reduction of Einstein's field equations for twisting typeN-vacuum fields with anH 2

The problem of vacuum typeN solutions of Einstein's field equations with Killing vector and homothetic group can be reduced to a single ordinary differential equation of the third order for a single real function. Hauser's solution 4] is an exceptional case. If the homothetic parameterN takes the valueN=2 the third order differential equation becomes surprisingly simple. This caseN=2 is therefore the most promising one for the search of exact solutions.