Solvable Lie algebras are not that hypo
Abstract
We study a type of left-invariant structure on Lie groups, or equivalently on Lie algebras. We introduce obstructions to the existence of a hypo structure, namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3). The choice of a splitting g^*=V_1 + V_2, and the vanishing of certain associated cohomology groups, determine a first obstruction. We also construct necessary conditions for the existence of a hypo structure with a fixed almost-contact form. For non-unimodular Lie algebras, we derive an obstruction to the existence of a hypo structure, with no choice involved. We apply these methods to classify solvable Lie algebras that admit a hypo structure.
Cite
@article{arxiv.1002.2177,
title = {Solvable Lie algebras are not that hypo},
author = {Diego Conti and Marisa Fernandez and Jose A. Santisteban},
journal= {arXiv preprint arXiv:1002.2177},
year = {2011}
}
Comments
21 pages; v2: presentation improved, typos corrected, notational conflicts eliminated. To appear in Transformation Groups