Related papers: Dirac operators with torsion, spectral Einstein fu…
In this paper, we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary. Furthermore, we provide the proof of the Dabrowski-Sitarz-Zalecki type theorems associated with the spectral…
In this paper, we compute the spectral Einstein functional associated with the Dirac operator with torsion on even-dimensional spin manifolds without boundary.
We investigate spectral functionals associated with Dirac and Laplace-type differential operators on manifolds, defined via the Wodzicki residue, extending classical results for Dirac operators derived from the Levi-Civita connection to…
The spectral metric and Einstein functionals defined by two vector fields and Laplace-type operators over vector bundles, giving an interesting example of the spinor connection and square of the Dirac operator. Motivated by the spectral…
In this paper, we define the spectral Einstein functional associated with the sub-Dirac operator for manifolds with boundary. A proof of the Dabrowski-Sitarz-Zalecki type theorem for spectral Einstein functions associated with the sub-Dirac…
For two one-forms and the Dirac operator, Dabrowski etc. recovered the spectral Einstein functionals by computing their noncommutative residue in Theorem 4.1 \cite{DL}. In this paper, we generalize the results of Dabrowski etc. to the cases…
In this paper, we define the spectral Einstein functional associated with the Dirac operator for manifolds with boundary. And we give the proof of Kastler-Kalau-Walze type theorem for the spectral Einstein functional associated with the…
In this paper, we derive some spectral (0,4)-tensor functionals by four one-forms and the Dirac operator and the noncommutative residue on even-dimensional compact spin manifolds without boundary. Then, we extend these spectral (0,4)-tensor…
In this paper, a simple proof of the divergence theorem is given by using the Dirac operator and noncommutative residues. Then we extend the divergence theorem to compact manifolds with boundary by the noncommutative residue of the…
In the paper, we give four different examples of the rescaled Dirac operator by the perturbation of the function f. Further, based on the trilinear Clifford multiplication by functional of differential one-forms, we compute the spectral…
We examine the metric and Einstein bilinear functionals of differential forms introduced in Adv.Math.,Vol.427,(2023)1091286, for Hodge-Dirac operator $d+\delta$ on an oriented even-dimensional Riemannian manifold. We show that they…
Inspired by statistical de Rham Hodge operators and the spectral functionals, we carry on some promotion to spectral functionals to noncommutative fields, and associate them with the noncommutative residue on manifolds with boundary. We…
We review the construction of the Dirac operator and its properties in Riemannian geometry and show how the asymptotic expansion of the trace of the heat kernel determines the spectral invariants of the Dirac operator and its index. We also…
The spectral torsion is defined by three vector fields and Dirac operators and the noncommutative residue. Motivated by the spectral torsion and the one form rescaled Dirac operator, we give some new spectral torsion which is the extension…
In this paper, we investigate some new spectral torsion which is the extension of spectral torsion for Dirac operators, and compute the spectral torsion associated with nonminimal de Rham-Hodge operators on manifolds with (or without)…
We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally…
We derive a formula for the gravitational part of the spectral action for Dirac operators on 4-dimensional manifolds with totally anti-symmetric torsion. We find that the torsion becomes dynamical and couples to the traceless part of the…
In [17], we obtained the spectral Einstein functional associated with the Dirac operator for n-dimensional manifolds without boundary. In this paper, we give the proof of general Dabrowski-Sitarz-Zalecki type theorems for the spectral…
This paper aims to provide an explicit computation of the equivariant noncommutative residue density of which yield the metric and Einstein tensors on even-dimensional Riemannian manifolds. A considerable contribution of this paper is the…
We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition…