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arXiv · 1910.09306

On the Koszul formula in noncommutative geometry

Jyotishman Bhowmick·Debashish Goswami·Giovanni Landi
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Abstract

We prove a Koszul formula for the Levi-Civita connection for any pseudo-Riemannian bilinear metric on a class of centered bimodule of noncommutative one-forms. As an application to the Koszul formula, we show that our Levi-Civita connection is a bimodule connection. We construct a spectral triple on a fuzzy sphere and compute the scalar curvature for the Levi-Civita connection associated to a canonical metric.

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Jyotishman Bhowmick, Debashish Goswami, Giovanni Landi. 2019-10-21. On the Koszul formula in noncommutative geometry. https://doi.org/10.1142/s0129055x20500324

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