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arXiv · 2104.07570

Levi-Civita connections from toral actions

Suvrajit Bhattacharjee·Soumalya Joardar·Sugato Mukhopadhyay
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Abstract

We construct tame differential calculi coming from toral actions on a class of $\mathrm{C}^*$-algebras. Relying on the existence of a unique Levi-Civita connection on such a calculus, we prove a version of the Bianchi identity. A Gauss-Bonnet theorem for the canonical tame calculus of rank two is studied.

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Suvrajit Bhattacharjee, Soumalya Joardar, Sugato Mukhopadhyay. 2021-04-15. Levi-Civita connections from toral actions. https://doi.org/10.1016/j.geomphys.2022.104650

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