One-forms, spectral Einstein functionals and the noncommutative residue

TL;DR

This paper extends the computation of spectral Einstein functionals, originally done for two one-forms and the Dirac operator, to four-dimensional spin manifolds with boundary using noncommutative residue techniques.

Contribution

It generalizes previous results to include four-dimensional spin manifolds with boundary, broadening the applicability of spectral Einstein functional analysis.

Findings

Extended spectral Einstein functional computations to manifolds with boundary

Demonstrated the use of noncommutative residue in new geometric contexts

Provided explicit formulas for four-dimensional cases

Abstract

For two one-forms and the Dirac operator, Dabrowski etc. recovered the spectral Einstein functionals by computing their noncommutative residue in Theorem 4.1 \cite{DL}. In this paper, we generalize the results of Dabrowski etc. to the cases of four dimensional spin manifolds with boundary.