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A new look at Levi-Civita connection in noncommutative geometry

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.

preprint2021arXivOpen access
Jyotishman BhowmickDebashish GoswamiSoumalya Joardar
math.QA
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Jyotishman BhowmickDebashish GoswamiSoumalya Joardar

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