接触李群中的格与5维接触可解流形
微分几何
2015-04-29 v3
摘要
本文研究了由接触李群均匀化的紧致接触流形的几何，即紧致流形，它是某个具有左不变接触结构的李群G与一个均匀格子子群的商。我们重新审视了Alexander关于可解李群上格子存在性的判据，并结合其他一些众所周知的工具加以应用，利用这些结果证明了在维数5中，恰好存在七个具有均匀格子的连通且单连通的接触李群，它们都是可解的。此外，还探讨了辛边界的问题。同时证明了特殊仿射群没有均匀格子。
引用
@article{arxiv.0904.3113,
title = {Lattices in contact Lie groups and 5-dimensional contact solvmanifolds},
author = {Andre Diatta and Brendan Foreman},
journal= {arXiv preprint arXiv:0904.3113},
year = {2015}
}
备注
V3: 19 pages. Latex. Former Section 5 from V1 and V2 has now been removed. We thank Dr Chris Wendl and Prof. Patrick Massot for constructive remarks that have led to some reconsiderations on former Section 5 of V2. Last version appeared at Kodai Mathematical Journal