This is a very nice and clearly written survey article. The first three sections give a background on Weyl geometry, quaternionic Hermitian manifolds and \(3\)-Sasakian manifolds. The main section is devoted to quaternion Hermitian Weyl and hyper-Hermitian Weyl manifolds. After giving necessary definitions, the most important properties are presented, next the canonical foliations and the structure theorems are discussed, especially, the links with \(3\)-Sasakian geometry and quaternion Kähler geometry, and homogeneous compact hyper-Hermitian Weyl manifolds.
For the entire collection see [Zbl 1001.00008].