Heavens and their integral manifolds

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Abstract
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.

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