Geometry of solutions to the c-projective metrizability equation

On an almost complex manifold, a quasi-Kähler metric, with canonical connection in the c-projective class of given minimal connection, is equivalent to nondegenerate solution c-projectively invariant metrizability equation. For this overdetermined equation, replacing maximal rank condition on solutions nondegeneracy prolonged system yields strictly wider non-vanishing (generalized) scalar curvature. We study geometries induced by solutions. each solution, strict point-wise signature partitions underlying manifold into strata, manner that generalizes model, certain Lie group orbit decomposition $$\mathbb{C}\mathbb{P}^m$$ . describe smooth nature and geometric structure strata component, generalizing embedded orbits model. This includes metric open components becomes singular at boundary. The closed inherit CR-structures can be viewed as infinity for metric.