A new look at Levi-Civita connection in noncommutative geometry

Authors

Jyotishman Bhowmick, Indian Statistical Institute, Kolkata
Debashish Goswami, Indian Statistical Institute, Kolkata
Soumalya Joardar, Indian Institute of Science Education and Research Kolkata

Article Type

Research Article

Publication Title

International Journal of Geometric Methods in Modern Physics

Abstract

We prove the existence and uniqueness of Levi-Civita connections for strongly σ-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 [J. Bhowmick, D. Goswami and S. Mukhopadhyay, Levi-Civita connections for a class of spectral triples, Lett. Math. Phys. 110 (2020) 835-884] and [J. Bhowmick, D. Goswami and G. Landi, On the Koszul formula in noncommutative geometry, Rev. Math. Phys. 32(10) (2020) 2050032].

DOI

10.1142/S021988782150105X

Publication Date

6-1-2021

Comments

Open Access, Green

Recommended Citation

Bhowmick, Jyotishman; Goswami, Debashish; and Joardar, Soumalya, "A new look at Levi-Civita connection in noncommutative geometry" (2021). Journal Articles. 1942.
https://digitalcommons.isical.ac.in/journal-articles/1942