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].

中文翻译：

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重新审视非对易几何中的 Levi-Civita 连接

我们证明了 Levi-Civita 连接的存在性和唯一性σ-兼容的伪黎曼度量驯服微分演算。这种伪黎曼度量正确地包含双线性度量的类别以及它们的保形变形。这扩展了 [J. Bhowmick，D. Goswami 和 S. Mukhopadhyay，一类光谱三元组的 Levi-Civita 连接，莱特。数学。物理。 110(2020) 835–884] 和 [J. Bhowmick、D. Goswami 和 G. Landi，关于非对易几何中的 Koszul 公式，转数学。物理。 32(10)(2020)2050032]。