Nearly integrable SO(3)-structures on 5-dimensional Lie groups
Differential Geometry
2012-01-04 v1
Abstract
Recent work Bobienski-Nurowski on 5-dimensional Riemannian manifolds with an SO(3) structure prompts us to investigate which Lie groups admit such a geometry. The case in which the SO(3) structure admits a compatible connection with torsion is considered. This leads to a classification under special behaviour of the onnection, which enables to recover all known examples, plus others bearing torsion of pure type. Suggestive relations with special structures in other dimensions are highlighted, with attention to eight-dimensional SU(3) geometry.
Keywords
Cite
@article{arxiv.math/0607392,
title = {Nearly integrable SO(3)-structures on 5-dimensional Lie groups},
author = {Anna Fino and Simon Chiossi},
journal= {arXiv preprint arXiv:math/0607392},
year = {2012}
}
Comments
22 pages