幂零群在伪黎曼流形上的共形作用
微分几何
2019-12-19 v2 动力系统
摘要
我们研究连通幂零李群在紧致伪黎曼流形上的共形作用。我们证明，若一个(p,q)型紧致流形M支持连通幂零群H的共形作用，则在p ≤ q的假设下，H的幂零度至多为2p+1；进一步，若达到该最大幂零度，则M在有限覆盖意义下共形等价于万有的(p,q)型紧致共形平坦空间。证明利用了与伪黎曼共形结构相关联的典范Cartan几何。
引用
@article{arxiv.0807.4735,
title = {Conformal actions of nilpotent groups on pseudo-Riemannian manifolds},
author = {Charles Frances and Karin Melnick},
journal= {arXiv preprint arXiv:0807.4735},
year = {2019}
}
备注
41 pages, 3 figures. Article has been shortened from previous version, and several corrections have been made according to referees' suggestions