Harmonic structures and intrinsic torsion
Differential Geometry
2015-08-04 v2
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.
Cite
@article{arxiv.1308.4083,
title = {Harmonic structures and intrinsic torsion},
author = {Diego Conti and Thomas Bruun Madsen},
journal= {arXiv preprint arXiv:1308.4083},
year = {2015}
}
Comments
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