非交换几何中 Levi-Civita 联络的新视角
量子代数
2021-01-20 v6
摘要
我们证明了在驯服微分演算上，强 sigma-相容伪黎曼度量的 Levi-Civita 联络的存在性与唯一性。此类伪黎曼度量真包含双线性度量及其共形变形类。这推广了参考文献 9 和 10 中的先前结果。本文还讨论了双线性伪黎曼度量的 Levi-Civita 联络的星相容性。
引用
@article{arxiv.1606.08142,
title = {A new look at Levi-Civita connection in noncommutative geometry},
author = {Jyotishman Bhowmick and Debashish Goswami and Soumalya Joardar},
journal= {arXiv preprint arXiv:1606.08142},
year = {2021}
}
备注
The original article has been split into two parts. The other part is arXiv 2101.07221. This version includes new results on star-compatibility of Levi-Civita connections. The main result holds for strongly \sigma-compatible metrics. This version is to be viewed as a follow up to references 9, 10, 11 and 13