Dabrowski et al. [Spectral metric and Einstein functionals for Hodge–Dirac operator, preprint (2023), arXiv:2307.14877] gave spectral Einstein bilinear functionals of differential forms for the Hodge–Dirac operator $d+\delta$ on an oriented even-dimensional Riemannian manifold. In this paper, we generalize the results of Dabrowski et al. to the cases of 4-dimensional oriented Riemannian manifolds with boundary. Furthermore, we give the proof of Dabrowski–Sitarz–Zalecki-type theorems associated with the Hodge–Dirac operator for manifolds with boundary.

中文翻译：

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边界流形的 Hodge–Dirac 算子和 Dabrowski–Sitarz–Zalecki 型定理

达布罗斯基等人。[Hodge–Dirac 算子的谱度量和爱因斯坦泛函，预印本 (2023)，arXiv:2307.14877] 给出了 Hodge–Dirac 算子微分形式的谱爱因斯坦双线性泛函$d+\delta$在有向偶维黎曼流形上。在本文中，我们概括了 Dabrowski等人的结果。具有边界的 4 维定向黎曼流形的情况。此外，我们给出了与边界流形的 Hodge-Dirac 算子相关的 Dabrowski-Sitarz-Zalecki 型定理的证明。