A Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator

Abstract

In this paper, we give a Lichnerowicz type formula for the J-twist D J of the Dirac operator. And we prove 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.

A Kastler–Kalau–Walze Type Theorem for the J-Twist $$D_{J}$$ of the Dirac Operator

“…Theorem 2.2. [21] If M is a n-dimensional almost product Riemannian spin manifold without boundary, we have the following:…”

“…By simple calculations, the leading symbol of the J-twist D J of the Dirac operator is not √ −1c(ξ). In [21,22], Liu and Wang proved the Kastler-Kalau-Walze type theorems for the J-twist D J of the Dirac operator on almost product Riemannian spin manifold with boundary. Zhang introduced the definition of an elliptic differential operator-Witten deformation in [23].…”