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By using the apparatus of exterior forms, a new spinorial notation and Cartan’s theory of integral manifolds, some new results concerning complex strong heavenly metrics are established. In particular, the study of a subfamily of two-variable heavens (type G-−, D-−, and N-−) is reduced to linear equations, a prolongation process related to first and second heavenly equaions is studied leading to a (presumably) infinite heirarchy of 1−forms, and finally, the symmetries of the studied structure are investigated from the point of view of its description by Pfafian forms, elucidating in this way previous results concerning Killing vectors.
Boyer et al. (Sun,) studied this question.
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