Homogeneous four-manifolds with half-harmonic Weyl curvature tensor

We show that a four-dimensional homogeneous manifold with half-harmonic Weyl curvature tensor is symmetric or homothetic either to the only nonsymmetric anti-self-dual homogeneous manifold or to the 3-symmetric space.

Automated summary

We demonstrate that a four-dimensional homogeneous manifold with a half-harmonic Weyl curvature tensor is either symmetric or homothetic, and it can be isomorphic to either the only nonsymmetric anti-self-dual homogeneous manifold or the 3-symmetric space.