论文标题
均匀的三维里曼尼亚空间
Homogeneous three-dimensional Riemannian spaces
论文作者
论文摘要
三维riemannian度量的必要条件，可以接受一组及异构体的群体。这些条件是内在的，演绎的，显性的和算法的，它们提供了这些几何形状的理想标记。结果表明，该组的及传递作用自然属于Bianchi-Behr分类中十种类型中的某些类型中的一些。根据RICCI张量，明确条件是所有这些类型的特征。
The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a transitive group of isometries are obtained. These conditions are Intrinsic, Deductive, Explicit and ALgorithmic, and they offer an IDEAL labeling of these geometries. It is shown that the transitive action of the group naturally falls into an unfolding of some of the ten types in the Bianchi-Behr classification. Explicit conditions, depending on the Ricci tensor, are obtained that characterize all these types.
