Nilmanifolds with a calibrated G_2-structure
Differential Geometry
2011-08-12 v2
Abstract
We introduce obstructions to the existence of a calibrated G_2-structure on a Lie algebra g of dimension seven, not necessarily nilpotent. In particular, we prove that if there is a Lie algebra epimorphism from g to a six-dimensional Lie algebra h with kernel contained in the center of g, then h has a symplectic form. As a consequence, we obtain a classification of the nilpotent Lie algebras that admit a calibrated G_2-structure.
Cite
@article{arxiv.1008.0797,
title = {Nilmanifolds with a calibrated G_2-structure},
author = {Diego Conti and Marisa Fernández},
journal= {arXiv preprint arXiv:1008.0797},
year = {2011}
}
Comments
21 pages; v2: added some introductory details on G_2 structures in Section 2, exposition improved. To appear in Differential Geometry and its Applications