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HARMONIC STRUCTURES AND INTRINSIC TORSION

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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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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Universit_a di Milano Bicocca, Via Cozzi 55, 20125, Milano, Italy

    DIEGO CONTI

  2. Department of Mathematics, Aarhus University, Ny Munkegade 118 Bldg. 1530, 8000, Aarhus C, Denmark

    THOMAS BRUUN MADSEN

Authors
  1. DIEGO CONTI
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  2. THOMAS BRUUN MADSEN
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Corresponding authors

Correspondence to DIEGO CONTI or THOMAS BRUUN MADSEN.

Additional information

This work was partially supported by FIRB 2012 “Geometria differenziale e teoria geometrica delle funzioni” and PRIN 2010-2011 “Varietà reali e complesse: geometria, topologia e analisi armonica”.

TBM thankfully acknowledges financial support from the Danish Council for Independent Research, Natural Sciences.

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CONTI, D., MADSEN, T.B. HARMONIC STRUCTURES AND INTRINSIC TORSION. Transformation Groups 20, 699–723 (2015). https://doi.org/10.1007/s00031-015-9325-x

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