In this paper, we classify 8-dimensional manifolds M admitting an SU(3) action of cohomogeneity one such that (i) M is simply connected and the orbit space M/G is isomorphic to [0, 1], and (ii) M/G ∼= S and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU(3) and to 8-dimensional quaternion-Kähler spaces. MSC classification: 57S25; 22E46, 5...

We investigate the geometry of Hermitian manifolds endowed with a compact Lie group action by holomorphic isometries principal orbits codimension one. In particular, we focus on special class these constructed following B\'erard-Bergery which includes, among others, line bundles $\mathbb C\mathbb P^{m-1}$, linear Hopf and Hirzebruch surfaces. characterize their invariant metrics, such as balanc...

In this paper, we give a classification of non simply connected seven dimensional Reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. We characterize the acting groups and describe the orbits. The first and second homo-topy groups of the orbits have been presented as well.