Abstract
Dabrowski et al. [Spectral metric and Einstein functionals for HodgeâDirac operator, preprint (2023), arXiv:2307.14877] gave spectral Einstein bilinear functionals of differential forms for the HodgeâDirac operator [Formula: see text] 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 DabrowskiâSitarzâZalecki-type theorems associated with the HodgeâDirac operator for manifolds with boundary.
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