D.V. Alekseevsky, F. Podest`a
Compact Cohomogeneity One Riemannian Manifolds of Positive Euler Characteristic and Quaternionic Kaehler Manifolds
The paper is published: in: "Geometry, topology and physics (Campinas, 1996)", de Gruyter, (1997), 1-33

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)

53C30 Homogeneous manifolds, See also {14M15, 14M17, 32M10,

Abstract: We investigate compact manifolds with positive Euler
characteristic which admit a smooth action of a compact Lie group
$G$ with codimension one orbit. We give a classification for a large class
of such $G$-manifolds up to a diffeomorphism and we apply
the classification to the case of $G$-manifolds with an invariant quaternionic K\"ahler structure.