Title

A new look at Levi-Civita connection in noncommutative geometry

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

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