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arXiv · 2206.02587

Spectral Metric and Einstein Functionals

Ludwik Dąbrowski·Andrzej Sitarz·Paweł Zalecki
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Abstract

We define bilinear functionals of vector fields and differential forms, the densities of which yield the metric and Einstein tensors on even-dimensional Riemannian manifolds. We generalise these concepts in non-commutative geometry and, in particular, we prove that for the conformally rescaled geometry of the noncommutative two-torus the Einstein functional vanishes.

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Ludwik Dąbrowski, Andrzej Sitarz, Paweł Zalecki. 2022-06-03. Spectral Metric and Einstein Functionals. https://doi.org/10.1016/j.aim.2023.109128

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