Harmonic structures and intrinsic torsion
arXiv:1308.4083 · doi:10.1007/s00031-015-9325-x
Abstract
We discuss the construction of Sp(2)Sp(1)-structures whose fundamental form is closed. In particular, we find 10 new examples of 8-dimensional nilmanifolds that admit an invariant closed 4-form with stabiliser Sp(2)Sp(1). Our constructions entail the notion of SO(4)-structures on 7-manifolds. We present a thorough investigation of the intrinsic torsion of such structures, leading to the construction of explicit Lie group examples with invariant intrinsic torsion.
24 pages; v2, added two remarks concerning a potential analogous construction related to Spin(7) and the existence of a lattice in the solvable examples. To appear in Transformation Groups