Harmonic structures and intrinsic torsion

TL;DR

This paper explores special geometric structures on manifolds, introducing new examples of 8-dimensional nilmanifolds with invariant closed forms and analyzing their intrinsic torsion properties.

Contribution

It constructs 10 new 8-dimensional nilmanifolds with Sp(2)Sp(1)-structures and investigates the intrinsic torsion of SO(4)-structures on 7-manifolds.

Findings

Found 10 new nilmanifolds with invariant closed 4-forms

Developed explicit Lie group examples with invariant intrinsic torsion

Analyzed the intrinsic torsion of SO(4)-structures

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.