Inner fluctuations and the spectral Einstein functional
Abstract
The spectral metric and Einstein functionals defined by two vector fields and Laplace-type operators over vector bundles, giving an interesting example of the spinor connection and square of the Dirac operator. Motivated by the spectral functionals and Dirac operators with inner fluctuations, we give some new spectral functionals which is the extension of spectral functionals for Dirac operators, and compute the spectral Einstein functional for the Dirac operator with inner fluctuations on even-dimensional spin manifolds without boundary.
Cite
@article{arxiv.2501.02253,
title = {Inner fluctuations and the spectral Einstein functional},
author = {Jian Wang and Yong Wang},
journal= {arXiv preprint arXiv:2501.02253},
year = {2025}
}
Comments
While the paper is certainly of interest and worth exploring, particularly in the context of noncommutative geometry, the results presented in the manuscript appear to be derivable from existing literature. More importantly, the approach adopted by the authors contains significant flaws, and the main result is, in fact, incorrect