A Kastler-Kalau-Walze type theorem for the $J$-twist of the Dirac operator with torsion

TL;DR

This paper establishes a Kastler-Kalau-Walze type theorem for the J-twisted Dirac operator with torsion on specific low-dimensional manifolds, extending geometric analysis in spin geometry.

Contribution

It introduces a Lichnerowicz formula and proves a Kastler-Kalau-Walze theorem for the J-twisted Dirac operator with torsion on 4D and 6D almost product Riemannian spin manifolds with boundary.

Findings

Derived a Lichnerowicz type formula for the J-twist of the Dirac operator with torsion.

Proved a Kastler-Kalau-Walze type theorem in 4D and 6D cases.

Extended geometric analysis to manifolds with boundary and torsion.

Abstract

In this paper, we give a Lichnerowicz type formula for the $J$-twist of the Dirac operator with torsion. And we prove a Kastler-Kalau-Walze type theorem for the $J$-twist of the Dirac operator with torsion on 4-dimensional and 6-dimensional almost product Riemannian spin manifold with boundary.