Riemannian manifolds with structure group PSU(3)
arXiv:1007.1205 · doi:10.1112/jlms/jdr044
Abstract
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.
24 pages