English

Balanced Hermitian geometry on 6-dimensional nilmanifolds

Differential Geometry 2012-12-05 v3

Abstract

The invariant balanced Hermitian geometry of nilmanifolds of dimension 6 is described. We prove that the holonomy group of the associated Bismut connection reduces to a proper subgroup of SU(3) if and only if the complex structure is abelian. As an application we show that if J is abelian then any invariant balanced J-Hermitian structure provides solutions of the Strominger system.

Keywords

Cite

@article{arxiv.1104.5524,
  title  = {Balanced Hermitian geometry on 6-dimensional nilmanifolds},
  author = {Luis Ugarte and Raquel Villacampa},
  journal= {arXiv preprint arXiv:1104.5524},
  year   = {2012}
}

Comments

23 pages; new section added, to appear in Forum Math

R2 v1 2026-06-21T18:00:10.582Z