The Rescaled Dirac operator fDh and the noncommutative residue for 6-dimensional manifolds

TL;DR

This paper calculates the noncommutative residue for a rescaled Dirac operator on 6-dimensional manifolds and proves a related Kastler-Kalau-Walze type theorem, extending understanding of geometric invariants in noncommutative geometry.

Contribution

It provides explicit residue calculations for the rescaled Dirac operator on 6-dimensional manifolds and establishes a Kastler-Kalau-Walze type theorem in this context.

Findings

Computed noncommutative residue for fDh on 6D manifolds

Proved Kastler-Kalau-Walze type theorem for fDh with boundary

Derived special cases solvable by the developed methods

Abstract

In this paper, we compute the noncommutative residue for the rescaled Dirac operator fDh on 6-dimensional compact manifolds without boundary. And we give the proof of the Kastler-Kalau-Walze type theorem for the rescaled Dirac operator fDh on 6-dimensional compact manifolds with boundary. We also give some important special cases which can be solved by our calculation methods.