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

The (4n + 3)-dimensional sphere S4n+3 can be viewed as the boundary of the quaternionic hyperbolic space H-H(n+1) and the group PSp(n + 1, 1) of quaternionic hyperbolic isometries extends to a real analytic transitive action on S4n+3. We call the pair (PSp(n + 1, 1),S4n+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. (C) 2003 Elsevier B.V. All rights reserved.