7 citations · 18 across the 25 of their papers we have counts for
27 papers
Mod 3 Congruence Families for twisted signatures of string manifolds in dimensions up to twenty-eight
Tong Wu, Yong Wang
In the paper, we establish congruences for twisted Dirac indices and signatures on closed string manifolds by specializing the two-parameter modular forms of Liu and Wang to the ta…
The Einstein-Hilbert action for perturbed second-order spectral triples
Tong Wu, Yong Wang
In [6], the higher-order spectral triple and its relative K-homology were studied. Motivated by the Kastler-Kalau-Walze theorem, we propose an extension of the Einstein-Hilbert act…
The spectral torsion for the rescaled Dirac operator
Tong Wu, Yong Wang
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 funct…
The spectral Einstein functional for the Witten Deformation
Tong Wu, Yong Wang
In the paper, given two vector fields and the Witten deformation, we compute the spectral Einstein functional for the Witten deformation on even-dimensional spin manifolds without…
The linear perturbation of the metric and the bimetric conformal invarints
Tong Wu, Yong Wang
In this paper, we give a method to construct bimetric conformal invarints by the linear metric perturbations and the conformal invarints. And we compute the metric perturbations of…
The Rescaled Dirac operator fDh and the noncommutative residue for 6-dimensional manifolds
Tong Wu, Yong Wang
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-K…
The Connes-Chamseddine cycle and the noncommutative integral
Tong Wu, Yong Wang
In [5], Connes and Chamseddine defined a cycle in the general framework of noncommutative geometry. They computed this cycle for the Dirac operator on 4-dimensioanl manifolds. We p…
The pseudo-differential perturbations of the Dirac operator and the Kastler-Kalau-Walze type theorems
Tong Wu, Yong Wang
We define two types of pseudo-differential perturbations of the Dirac operator within the framework of the noncommutative geometry. And we obtain the noncommutative residue of the…
The general Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for odd dimensional manifold with boundary
Tong Wu, Yong Wang, Sining Wei
In this paper, we give the proof of the general Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem on odd dimensional compact manifolds with boundary.
The Hodge-Dirac operator and Dabrowski-Sitarz-Zalecki type theorems for manifolds with boundary
Tong Wu, Yong Wang
In [10], Dabrowski etc. gave spectral Einstein bilinear functionals of differential forms for the Hodge-Dirac operator on an oriented even-dimensional Riemannian manifold. In…
A general Dabrowski-Sitarz-Zalecki type theorems for manifold with boundary
Tong Wu, Yong Wang
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 D…
Dirac operators with torsion, spectral Einstein functionals and the noncommutative residue
Jian Wang, Yong Wang, Tong Wu
Recently Dabrowski etc. \cite{DL} obtained the metric and Einstein functionals by two vector fields and Laplace-type operators over vector bundles, giving an interesting example of…
One-forms, spectral Einstein functionals and the noncommutative residue
Jian Wang, Yong Wang, Tong Wu +2
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 pap…
Riemannian geometry of noncommutative super surfaces
Yong Wang, Tong Wu
In this paper, a Riemannian geometry of noncommutative super surfaces is developed which generalizes [4] to the super case. The notions of metric and connections on such noncommuta…
The spectral Einstein functional and the noncommutative residue for manifolds with boundary
Tong Wu, Yong Wang
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…
Affine connections on singular multiply warped products and singular twisted products
Siyao Liu, Tong Wu, Yong Wang
In this paper, we generalize the results in [Y. Wang: Affine connections on singular warped products. Int. J. Geom. Methods Mod. Phys. 18(5), 2150076, (2021).] to singular multiply…
Super twisted products
Tong Wu, Yong Wang, Xue Wang
In this paper, we define the -curvature tensor on super Riemannian manifolds. And we compute the curvature tensor, the Ricci tensor and the -curvature tensor on super twi…
The generalized noncommutative residue and the Kastler-Kalau-Walze type theorem
Tong Wu, Yong Wang
In this paper, we define the generalized noncommutative residue of the Dirac operator. And we give the proof of Kastler-Kalau-Walze type theorems for the generalized noncommutative…
A Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator
Siyao Liu, Yong Wang
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 opera…
The perturbation of the de Rham Hodge Operator and the Kastler-Kalau-Walze type theorem for manifolds with boundary
Siyao Liu, Tong Wu, Yong Wang
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…
Super warped products with a semi-symmetric non-metric connection
Tong Wu, Yong Wang
In this paper, we define a semi-symmetric non-metric connection on super Riemannian manifolds. And we compute the curvature tensor and the Ricci tensor of a semi-symmetric non-metr…
The operator and the Kastler-Kalau-Walze type theorems
Tong Wu, Yong Wang
In this paper, we obtain two Lichnerowicz type formulas for the operators and . And we give the proof of Kastler-Kalau…
Gauss-Bonnet theorems associated to deformed Schouten-Van Kampen connection in the affine group and the group of rigid motions of the Minkowski plane
Tong Wu, Yong Wang
In this paper, we define deformed Schouten-Van Kampen connections which are metric connections and compute sub-Riemannian limits of Gaussian curvature for a Euclidean C2-smooth sur…
Codazzi tensors and the quasi-statistical structure associated to affine connections on three-dimensional Lorentzian Lie groups
Tong Wu, Yong Wang
In this paper, we classify three-dimensional Lorentzian Lie groups on which Ricci tensors associated to Bott connections, canonical connections and Kobayashi-Nomizu connections are…