Spectral Metric and Einstein Functionals

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.

Final version, typos corrected

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Cited by in corpus (6)

• Gauge theories on quantum spaces
• Spectral Torsion
• Dirac operators with torsion, spectral Einstein functionals and the noncommutative residue
• Spectral forms and de-Rham Hodge operator
• The Spectral Einstein functional and Kastler-Kalau-Walze type theorems
• Equivariant Bismut Laplacian and spectral Einstein functional