On certain locally homogeneous Clifford manifolds
A Clifford structure of order \(m\) on a connected differentiable manifold \(M\) is a family of \(m\) anticommuting complex structures generating a subalgebra of dimension 2 of \(\text{End} (T(M))\). In this paper, the authors investigate the existence of locally invariant Clifford structures of order \(m \geq 2\) on a class of locally homogeneous manifolds. They study the case of solvable extensions of \(H\)-type groups, showing in particular that the solvable Lie groups corresponding to the symmetric spaces of negative curvature carry invariant Clifford structures of order \(m \geq 2\). They also show that for each \(m\) and any finite group \(F\), there is a compact flat manifold with holonomy group \(F\) and carrying a Clifford structure of order \(m\).
scientific article; zbMATH DE number 792880