1 Department of Mathematics, Science and Technology, Aarhus University2 Universita di Milano Bicocca3 Department of Mathematics, Science and Technology, Aarhus University
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.
Transformation Groups, 2015, Vol 20, Issue 3, p. 699-723