Tong Wu, Sining Wei, Yong Wang
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 (resp.without) boundary.
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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 this theorem to the general $n$ dimensional manifold. An equivariant Kastler-Kalau-Walze type theorem with torsion is also proved.
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 residue on 4-dimensional and 6-dimensional compact manifolds with (resp.without) boundary.
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 (resp.without) boundary
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 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 proved.
The Spectral Einstein functional and Kastler-Kalau-Walze type theorems
本文定义了带边界流形上与Dirac算子相关的谱爱因斯坦泛函，并证明了低维情形下的Kastler-Kalau-Walze型定理。
The general Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for odd dimensional manifold with boundary
本文证明了带边界的奇数维紧流形上的一般Kastler-Kalau-Walze型定理和Dabrowski-Sitarz-Zalecki型定理。
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 action for Witten deformation on 4-dimensional compact manifolds.
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 manifolds with boundary.
Conformal perturbations of dirac operators and general Kastler-Kalau-Walze type theorems for even dimensional manifolds with boundary
本文证明了带边与无边偶维紧流形上Dirac算子共形扰动的一般Kastler-Kalau-Walze型定理。
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 Riemannian spin manifold with boundary.
The Kastler-Kalau-Walze type theorems about J-Witten deformation
本文针对J-Witten变形建立Lichnerowicz型公式，并在四维与六维近乘积黎曼旋量流形上证明了带边界和不带边界情形下的Kastler-Kalau-Walze型定理。
In this paper, we obtain two Lichnerowicz type formulas for the operators $\sqrt{-1}\widehat{c}(V)(d+δ)$ and $-\sqrt{-1}(d+δ)\widehat{c}(V)$. And we give the proof of Kastler-Kalau-Walze type theorems for the operators $\sqrt{-1}\widehat{c}(V)(d+δ)$ and $-\sqrt{-1}(d+δ)\widehat{c}(V)$ on 3,4-dimensional oriented compact manifolds with (resp.without) boundary.
A Kastler-Kalau-Walze type theorem for the $J$-twist of the Dirac operator with torsion
该研究推导了带挠率的Dirac算子的$J$-扭的Lichnerowicz型公式，并在4维和6维带边界近乘积黎曼自旋流形上证明了对应的Kastler-Kalau-Walze型定理，拓展了非交换几何相关结果。
The general Kastler-Kalau-Walze type theorem for the J-twist DJ of the Dirac operator
本文推广了Dirac算子J-扭曲DJ的Kastler-Kalau-Walze型定理，从低维情形扩展到偶数维带边界的几乎乘积黎曼自旋流形，并给出一般证明。
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 compact manifolds with (resp.without) boundary. Some concrete examples of the perturbation of the de Rham Hodge operator are provided for our main theorems.
The J-twist D_J of the Dirac operator and the Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary
本文将已有三维、四维带边近积黎曼 spin 流形上关于 Dirac 算子 J-扭变 D_J 的 Kastler-Kalau-Walze 型定理推广到六维情形。
The pseudo-differential perturbations of the Dirac operator and the Kastler-Kalau-Walze type theorems
本文在非交换几何框架内定义了 Dirac 算子的两类伪微分扰动，推导了其在 4 维紧流形上的非交换留数，并证明了带边界流形上的 Kastler-Kalau-Walze 型定理。
In this paper, we establish some general Kastler-Kalau-Walze type theorems for any dimensional manifolds with boundary which generalize the results in [WW1].
Transformation operators and the Kastler-Kalau-Walze type theorems on 4-dimensional manifolds
该研究针对带边界4维流形，计算了变换算子的低维体积Vol(1,1)，并推导得出对应的Kastler-Kalau-Walze型定理，丰富了非交换几何与微分几何交叉领域的相关结果。
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 Kastler-Kalau-Walze type theorem in this case.
The bimetric spectral Einstein-Hilbert action and the Kastler-Kalau-Walze type theorem for Lorentz warped products
本文通过定义双度量谱爱因斯坦-希尔伯特作用量并计算其在Lorentz扭曲积上的值，建立了相应的Kastler-Kalau-Walze型定理。
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 on boundary. We also compute the spectral action for Dirac operators with two-form perturbations on $4$-dimensional compact manifolds.
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 noncommutative residue associated with Dirac operators.For 6-dimensional manifolds with boundary, we also get a Kastler-Kalau-Walze type theorem for a general fourth order operator.
The Bimetric generalization of Kastler--Kalau--Walze Type Theorems
本文推广Kastler--Kalau--Walze定理至双度量情形，计算Wodzicki留数，得到边界项为曲率差积分，度量重合时还原经典恒等式。
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 Dirac operator on 4-dimensional manifolds with boundary.
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 establish two kinds of Kastler-Kalau-Walze type theorems for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection on six-dimensional manifolds with boundary.
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 operators in this case.
In this paper, we obtain two kinds of Kastler-Kalau-Walze type theorems for conformal perturbations of twisted Dirac operators and conformal perturbations of signature operators by a vector bundle with a non-unitary connection on six-dimensional manifolds with (respectively without)boundary.
In this paper, we get a Kastler-Kalau-Walze type theorem associated to nonminimal de Rham-Hodge operators on compact manifolds with boundary. We give two kinds of operator-theoretic explanations of the gravitational action in the case of four dimensional compact manifolds with flat boundary.
The noncommutative residue and sub-Riemannian limits for the twisted BCV spaces
本文推导了扭曲BCV空间的Kastler-Kalau-Walze型与Dabrowski-Sitarz-Zalecki型定理的次黎曼版本，并计算了扭曲乘积的Connes共形不变量及其次黎曼极限。
Equivariant Twisted Bismut Laplacian with Torsion and KKW type theorems
本文研究带挠率的等变扭曲Bismut拉普拉斯算子的非交换留数密度显式计算问题，证明了带边界紧流形上带挠率的等变扭曲Kastler-Kalau-Walze型定理，为相关几何分析提供理论支撑。
The Rescaled Dirac operator fDh and the noncommutative residue for 6-dimensional manifolds
本文计算了6维紧流形上重标度Dirac算子fDh的非交换留数，证明了有边界情形的Kastler-Kalau-Walze型定理，并给出若干重要特例。
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 the case of 4-dimensional manifolds with flat boundary.
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 the gravitational action for boundary in the case of 4-dimensional manifolds with flat boundary. In particular, for 6-dimensional spin manifolds with boundary with the conformal Robertson-Walker metric, we obtain the noncommutative residue of the composition of $π^+D^{-1}$ and $π^+D^{-3}$ is proportional to the Einstein-Hilbert action for manifolds with bound…
In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and twisted signature operators on 4-dimensional manifolds with (resp. without) boundary.
In this paper, we define lower dimensional volumes associated to sub-Dirac operators for foliations. In some cases, we compute these lower dimensional volumes. We also prove the Kastler-Kalau-Walze type theorems for foliations with or without boundary. As a corollary, we give an explanation of the gravitational action for the Robertson-Walker space $[a, b]\times_{f}M^{3}$.
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