Closed -eigenforms and exact -structures

  • Marco Freibert

    Christian-Albrechts-Universität zu Kiel, Germany
  • Simon Salamon

    King's College London, UK
Closed $G_2$-eigenforms and exact $G_2$-structures cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

A study is made of left-invariant -structures with an exact 3-form on a Lie group whose Lie algebra admits a codimension-one nilpotent ideal . It is shown that such a Lie group cannot admit a left-invariant closed -eigenform for the Laplacian and that any compact solvmanifold arising from does not admit an (invariant) exact -structure. We also classify the seven-dimensional Lie algebras with codimension-one ideal equal to the complex Heisenberg Lie algebra which admit exact -structures with or without special torsion. To achieve these goals, we first determine the six-dimensional nilpotent Lie algebras admitting an exact -structure or a half-flat -structure with exact , respectively.

Cite this article

Marco Freibert, Simon Salamon, Closed -eigenforms and exact -structures. Rev. Mat. Iberoam. 38 (2022), no. 6, pp. 1827–1866

DOI 10.4171/RMI/1315