论文标题
在三维几乎爱因斯坦歧管上，带有循环结构
On 3-dimensional almost Einstein manifolds with circulant structures
论文作者
论文摘要
考虑了$（1,1）$的张量结构的三维Riemannian歧管，其第三个功率是身份。该结构和度量标准相对于某些基础具有循环矩阵，即这些结构是循环的。研究了一个相关的歧管，其指标均由两种结构表示。考虑了三类此类歧管。其中两个取决于歧管的曲率张量的特殊特性。第三类是由歧管组成的，其结构相对于度量的Levi-Civita连接是平行的。获得了这些歧管的一些几何特征。给出了这种歧管的例子。
A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e., these structures are circulant. An associated manifold, whose metric is expressed by both structures, is studied. Three classes of such manifolds are considered. Two of them are determined by special properties of the curvature tensor of the manifold. The third class is composed by manifolds whose structure is parallel with respect to the Levi-Civita connection of the metric. Some geometric characteristics of these manifolds are obtained. Examples of such manifolds are given.
