The J-twist D_J of the Dirac operator and the Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary

TL;DR

This paper extends the Kastler-Kalau-Walze type theorem to the J-twist Dirac operator on six-dimensional almost product Riemannian spin manifolds with boundary, generalizing previous results from lower dimensions.

Contribution

It develops a new Kastler-Kalau-Walze type theorem for the J-twist Dirac operator in six dimensions, expanding the understanding of spectral geometry on manifolds with boundary.

Findings

Established the theorem for 6-dimensional manifolds with boundary.

Generalized previous results from 3- and 4-dimensional cases.

Provided explicit formulas for the J-twist Dirac operator.

Abstract

In [22], the authors proved a Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator on 3-dimensional and 4-dimensional almost product Riemannian spin manifold with boundary. In this paper, we develop the Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator on a 6-dimensional almost product Riemannian spin manifold with boundary.