Riemannian manifolds with structure group PSU(3)

We study 8-dimensional Riemannian manifolds that admit a PSU(3)-structure. We classify these structures by their intrinsic torsion and characterize the corresponding classes via differential equations. Moreover, we consider a connection defined by a 3- and a 4-form that preserves the underlying structure. Finally, we discuss the geometry of these manifolds relatively to the holonomy algebra of this connection.