Abstract
In this article, we classify 7- and 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) \({M/G\cong S^{1}}\) and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU(3) and to 8-dimensional quaternion-Kahler spaces, and links between dimension 7 and 8 given by circle actions.
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