Quaternionic Kahler Manifolds, Constrained Instantons and the Magic Square: I

Understand

The classification of homogeneous quaternionic manifolds has been done by Alekseevskii, Wolf et al using transitive solvable group of isometries.

• These manifolds are not generically symmetric, but there is a subset of quaternionic manifolds that are symmetric and Einstein.
• A further subset of these manifolds are the magic square manifolds.
• We show that all the symmetric quaternionic manifolds including the magic square can be succinctly classified by constrained instantons.