Employing the spinorial approach to the structure of hyperheavens, we integrate completely the Killing vector equations for plane (case I) hyperheavens, reducing them to one master equation of an extremely plausible form. (In this process, optimally simple gauges are demonstrated for each Petrov type.) The mechanism of generating Ernst potentials by Killing vectors is then investigated, and explicit forms are given. Also, some interesting preliminary study of Killing spinors of type D (0,k) in heavens is presented.
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Finley et al. (1978) studied this question.
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