Related papers: A Kastler-Kalau-Walze Type Theorem for 7-dimension…
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 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…
We prove a Kastler-Kalau-Walze type theorem for the Dirac operator and the signature operator for $3,4$-dimensional manifolds with boundary. As a corollary, we give two kinds of operator theoretic explanations of the gravitational action in…
In this paper, we obtain a Lichnerowicz type formula for J-Witten deformation and give the proof of the Kastler-Kalau-Walze type theorems associated with J-Witten deformation on four-dimensional and six-dimensional almost product Riemannian…
In this paper, we prove a Kastler-Kalau-Walze type theorem for perturbations of Dirac operators on compact manifolds with or without boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action…
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 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 get the Kastler-Kalau-Walze theorem associated to Dirac operators with torsion on compact manifolds with boundary. We give two kinds of operator-theoretic explanations of the gravitational action in the case of…
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 [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 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 define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume ${\rm Vol}^{(2,2)}$ for 5-dimensional and 6-dimensional spin manifolds with boundary and we also get the…
The Kastler-Kalau-Walze theorem, announced by Alain Connes, shows that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein-Hilbert action of general relativity. In this paper, we prove a…
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.
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 prove a Kastler-Kalau-Walze type theorem for 4-dimensional and 6-dimensional spin manifolds with boundary associated with the conformal Robertson-Walker metric. And we give two kinds of operator theoretic explanations of…
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 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 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…