Walker's theorem without coordinates

Some symmetry properties of four-dimensional Walker manifolds

In this paper, we investigate geometric properties of some curvature tensors of a four-dimensional Walker manifold. Some characterization theorems are also obtained.

三维Walker流形上的Ricci-Yamabe孤立子

Ricci-Yamabe solitons on a Walker 3-manifold

本文研究三维Walker流形上的Ricci-Yamabe孤立子，通过带势函数的De-Rham霍奇分解求解孤立子场，完成了对应孤立子的分类并辅以例证。

Noncommutative Residue and Dirac operators for Manifolds with the Conformal Robertson-Walker metric

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…

Noncompactness and maximum mobility of type III Ricci-flat self-dual neutral Walker four-manifolds

It is shown that a self-dual neutral Einstein four-manifold of Petrov type III, admitting a two-dimensional null parallel distribution compatible with the orientation, cannot be compact or locally homogeneous, and its maximum possible degree of mobility is 3. Diaz-Ramos, Garcia-Rio and Vazquez-Lorenzo found a general coordinate form of such manifolds. The present paper also provides a modified version of that coordinate form, valid in a suitably defined generic case and, in a sense, "more canonical" than the usual formulation. Moreover, the local-isometry types of manifolds as above having the…

几乎para切触度量3维Walker流形

Almost paracontact metric 3-dimensional Walker manifolds

本文在3维Walker流形上构造几乎para切触度量结构，给出其属于各类别（如para切触、正规、para余辛等）的充要条件，并研究η-Einstein流形的曲率性质。

关于Walker流形的李流形结构

On the Lie Foliation structure of Walker Manifolds

本文研究Walker流形的结构，证明其null平行分布可积分为G-Lie流形，并探讨Ricci曲率与流形维度的关系，提出局部分类和刚性定理。