  We give a general Lie-theoretic construction for anti-invariant almost
Hermitian Riemannian submersions, anti-invariant quaternion Riemannian
submersions, anti-invariant para-Hermitian Riemannian submersions,
anti-invariant para-quaternion Riemannian submersions, and anti-invariant
octonian Riemannian submersions. This yields many compact Einstein examples.
