Spin(4) actions on $8$-dimensional manifolds (I)

Abstract

We study smooth Spin(4) actions on closed, orientable $8$-dimensional manifolds, where Spin(4) is isomorphic to the group $\mathrm{SU}(2) \times \mathrm{SU}(2)$. We examine the isotropy structures that can arise, and give an equivariant classification in the case where the set of exceptional orbits, stabilized by finite-cyclic goups, is empty.