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.
Spectral metric and Einstein functionals / Dabrowski, Ludwik; Sitarz, Andrzej; Zalecki, Pawel. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 427:(2023). [10.1016/j.aim.2023.109128]
Spectral metric and Einstein functionals
Ludwik Dabrowski;
2023-01-01
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.File in questo prodotto:
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