  We determine the space of algebraic pseudo-Hermitian K\"ahler-Weyl curvature
tensors and the space of para-Hermitian K\"ahler-Weyl curvature tensors in
dimension 4 and show that every algebraic possibility is geometrically
realizable. We establish the Gray identity for pseudo-Hermitian Weyl manifolds
and for para-Hermitian Weyl manifolds in arbitrary dimension.

Differential Geometry