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arxiv: 2206.02587 · v2 · pith:CY3BJLYT · submitted 2022-06-03 · math.DG · gr-qc· math-ph· math.MP· math.OA· math.QA

Spectral Metric and Einstein Functionals

Ludwik D\k{a}browski , Andrzej Sitarz , Pawe{\l} Zalecki This is my paper

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classification math.DG gr-qcmath-phmath.MPmath.OAmath.QA
keywords einsteinfunctionalsgeometrymetricbilinearconceptsconformallydefine
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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On Geometric Spectral Functionals

    math-ph 2025-05 unverdicted novelty 6.0

    Spectral functionals via Wodzicki residue recover geometric tensors including volume, metric, curvature and torsion on manifolds with torsion and yield chiral invariants.