Nearly integrable SO(3)-structures on 5-dimensional Lie groups
微分几何
2012-01-04 v1
摘要
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.
引用
@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}
}
备注
22 pages