The perturbation of the de Rham Hodge Operator and the Kastler-Kalau-Walze type theorem for manifolds with boundary

TL;DR

This paper establishes Kastler-Kalau-Walze type theorems for perturbed de Rham Hodge operators on 4- and 6-dimensional manifolds with boundary, extending geometric analysis results to new operator perturbations.

Contribution

It introduces Lichnerowicz type formulas for perturbed de Rham Hodge operators and proves related Kastler-Kalau-Walze theorems for manifolds with boundary, including concrete examples.

Findings

Kastler-Kalau-Walze theorems proven for 4D and 6D manifolds with boundary

Lichnerowicz type formulas derived for perturbed de Rham Hodge operators

Concrete examples illustrating the main theorems

Abstract

In this paper, we give Lichnerowicz type formulas for the perturbation of the de Rham Hodge operator. We prove the Kastler-Kalau-Walze type theorems for the perturbation of the de Rham Hodge operator on 4-dimensional and 6-dimensional compact manifolds with (resp.without) boundary. Some concrete examples of the perturbation of the de Rham Hodge operator are provided for our main theorems.