  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.
