English

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.

Keywords

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

R2 v1 2026-06-22T01:11:40.301Z