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Generalized Calabi–Gray manifolds are non-Kähler complex manifolds with very explicit geometry yet not being homogeneous. In this note, we demonstrate how generalized Calabi–Gray manifolds can be used to answer some questions in non-Kähler geometry.

This paper continues the study of non-general type subvarieties begun in a joint paper with Schneider and Sommese [14]. We prove uniruledness of a projective manifold containing a submanifold not of general type whose normal bundle has positivity properties and study moreover the rational quotient. We also relate the fundamental groups and a prove a cohomological criterion for a manifold to be rationally connected (weak version of a conjecture of Mumford).