A new look at Levi-Civita connection in noncommutative geometry
Quantum Algebra
2021-01-20 v6
Abstract
We prove the existence and uniqueness of Levi-Civita connections for strongly sigma-compatible pseudo-Riemannian metrics on tame differential calculi. Such pseudo-Riemannian metrics properly contain the classes of bilinear metrics as well as their conformal deformations. This extends the previous results in references 9 and 10. Star-compatibility of Levi-Civita connections for bilinear pseudo-Riemannian metrics are also discussed.
Keywords
Cite
@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}
}
Comments
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