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arXiv 2501.02253math.DG
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内涨落与谱爱因斯坦泛函

Inner fluctuations and the spectral Einstein functional

Jian Wang, Yong Wang

备注：
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
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AI总结：

本文受内涨落狄拉克算子启发，提出新的谱泛函作为狄拉克算子谱泛函的推广，并在无边界偶维自旋流形上计算了带内涨落的狄拉克算子的谱爱因斯坦泛函。

摘要：

由两个向量场和向量丛上的拉普拉斯型算子定义的谱度量与爱因斯坦泛函，给出了旋量联络和狄拉克算子平方的一个有趣例子。受谱泛函与带内涨落的狄拉克算子启发，我们给出了一些新的谱泛函，它们是狄拉克算子谱泛函的推广，并在无边界偶维自旋流形上计算了带内涨落的狄拉克算子的谱爱因斯坦泛函。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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