Three-dimensional Lie group actions on compact (4n+3)-dimensional geometric manifolds

The (4n+3)-dimensional sphere S^4n+3 can be viewed as the boundary of the quaternionic hyperbolic space H^n+1 H and the group PSp(n+1,1) of quaternionic hyperbolic isometries extends to a real analytic transitive action on S^4n+3. We call the pair (PSp(n+1,1),S^4n+3) a spherical Q C–C geometry. A manifold M locally modelled on this geometry is said to be a spherical Q C–C manifold. We shall classify all pairs (G,M) where G is a three-dimensional connected Lie group which acts smoothly and almost freely on a compact spherical Q C–C manifold M, preserving the geometric structure. As an application, we shall determine all compact 3-pseudo-Sasakian manifolds admitting spherical Q C–C structures.