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