相关论文: The Kastler-Kalau-Walze type theorems about J-Witt…

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…

In this paper, we give a Lichnerowicz type formula for the $J$-twist of the Dirac operator with torsion. And we prove a Kastler-Kalau-Walze type theorem for the $J$-twist of the Dirac operator with torsion on 4-dimensional and 6-dimensional…

In [22], the authors proved 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. In this paper, we develop the…

In [21] and [22], we proved the Kastler-Kalau-Walze type theorem for the J-twist DJ of the Dirac operator on 3-dimensional, 4-dimensional and 6-dimensional almost product Riemannian spin manifold with boundary. In this paper, we generalize…

In this paper, we obtain two Lichnerowicz type formulas for the Dirac-Witten operators. And we give the proof of Kastler-Kalau-Walze type theorems for the Dirac-Witten operators on 4-dimensional and 6- dimensional compact manifolds with…

In this paper, we give a brute-force proof of the Kastler-Kalau-Walze type theorem for $7$-dimensional manifolds with boundary about Witten deformation, and give a theoritic explaination of the gravitational action for $7$ dimensional…

In this paper, we prove an equivariant Kastler-Kalau-Walze type theorem for spin manifolds without boundary. For $6$ dimensional spin manifolds with boundary, we also give an equivariant Kastler-Kalau-Walze type theorem. Then we generalize…

In this paper, we give two Lichnerowicz type formulas for modified Novikov operators. We prove KastlerKalau-Walze type theorems for modified Novikov operators on compact manifolds with (resp.without) boundary. We also compute the spectral…

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…

In this paper, we give the Lichnerowicz type formulas for statistical de Rham Hodge operators. Moreover, Kastler-Kalau-Walze type theorems for statistical de Rham Hodge operators on compact manifolds with (respectively without) boundary are…

In this paper, we obtain two Lichnerowicz type formulas for sub-signature operators. And we give the proof of Kastler-Kalau-Walze type theorems for sub-signature operators on 4-dimensional and 6-dimensional compact manifolds with…

In this paper, we define lower dimensional volumes of compact Riemannian manifolds with boundary. For five dimensional spin manifolds with boundary, we prove a Kastler-Kalau-Walze type theorem associated with one-form perturbations of Dirac…

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.

In this paper, we establish some general Kastler-Kalau-Walze type theorems for any dimensional manifolds with boundary which generalize the results in [WW1].

In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume ${\rm Vol}_{6}^{(1,3)}$ for 6-dimensional spin manifolds with boundary and the gravity on boundary is derived by the…

In this paper, we prove two Kastler-Kalau-Walze type theorems for conformal perturbations of twisted Dirac operators and conformal perturbations of twisted signature operators on four-dimensional manifolds with (resp. without) boundary.

In this paper, we obtain two Lichnerowicz type formulas for the operators $\sqrt{-1}\widehat{c}(V)(d+\delta)$ and $-\sqrt{-1}(d+\delta)\widehat{c}(V)$. And we give the proof of Kastler-Kalau-Walze type theorems for the operators…

In this paper, we obtain two Kastler-Kalau-Walze type theorems for conformal perturbations of modified Novikov Operators on four-dimensional and six-dimensional compact manifolds with (respectively without)boundary.

In this paper, we establish the proof of general Kastler-Kalau-Walze type theorems for conformal perturbations of dirac Operators on even dimensional compact manifolds with (respectively without) boundary.

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 inverse square of these perturbations on 4-dimensional…