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

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.

arXiv commentarXiv admin note: text overlap with arXiv:2401.10909, arXiv:2111.15034, arXiv:2310.09775, arXiv:2406.14300, arXiv:2309.07558, arXiv:2312.00154