We discuss the construction of Sp(2) Sp(1)-structures whose fundamental form is closed. In particular, we fund 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.
Conti, D., Madsen, T. (2015). Harmonic structures and intrinsic torsion. TRANSFORMATION GROUPS, 20(3), 699-723 [10.1007/s00031-015-9325-x].
Harmonic structures and intrinsic torsion
CONTI, DIEGO
Primo
;
2015
Abstract
We discuss the construction of Sp(2) Sp(1)-structures whose fundamental form is closed. In particular, we fund 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.
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Conti Madsen - Harmonic structures and intrinsic torsion.pdf
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