The general Kastler-Kalau-Walze type theorem for the J-twist DJ of the Dirac operator

TL;DR

This paper extends the Kastler-Kalau-Walze theorem to the J-twist Dirac operator on even-dimensional almost product Riemannian spin manifolds with boundary, broadening its applicability in geometric analysis.

Contribution

It generalizes previous results to even-dimensional cases, providing a comprehensive proof for the J-twist Dirac operator on manifolds with boundary.

Findings

Established the Kastler-Kalau-Walze type theorem for even-dimensional manifolds

Extended previous results from specific dimensions to general even dimensions

Provided a proof framework for the J-twist Dirac operator on manifolds with boundary

Abstract

In [21] and [22], we proved the Kastler-Kalau-Walze type theorem for the J-twist DJ of the Dirac operator on 3-dimensional, 4-dimensional and 6-dimensional almost product Riemannian spin manifold with boundary. In this paper, we generalize our previous conclusions and establish the proof of the general Kastler-Kalau-Walze type theorem for the J-twist DJ of the Dirac operator on even-dimensional almost product Riemannian spin manifold with boundary.