论文标题
均质的riemannian歧管的结构无效
The structure of homogeneous Riemannian manifolds with nullity
论文作者
论文摘要
我们发现新的条件是，不可约合均匀空间的曲率张量的存在$ m = g/h $在lie代数$ \ mathfrak g $ of $ g $的lie代数$ \ mathfrak g $和lie elgebra $ \ tilde {\ tilde {\ mathfrak g} $的$ m $ m $ $ m $ $ m $ $。也就是说，我们证明存在$ m $在无效的任何元素方向上的传输，这可能是通过扩大演示组$ g $的。此外，我们证明这些转变会产生$ \ tilde {\ mathfrak g} $的Abelian理想。这些结果对\ cite {dov}中开发的结构理论构成了实质性的改进。此外，我们构建了具有非平凡无效的均质里曼尼亚空间的示例，其中$ g $是一个不可解决的群体，回答了一个自然的开放问题。这样的例子承认（本地同质）紧凑型商。对于共同杀害$ 3 $，我们对任何同质性不可还原的riemannian歧管的均衡组进行明确描述。
We find new conditions that the existence of nullity of the curvature tensor of an irreducible homogeneous space $M=G/H$ imposes on the Lie algebra $\mathfrak g$ of $G$ and on the Lie algebra $\tilde{\mathfrak g}$ of the full isometry group of $M$. Namely, we prove that there exists a transvection of $M$ in the direction of any element of the nullity, possibly by enlarging the presentation group $G$. Moreover, we prove that these transvections generate an abelian ideal of $\tilde{\mathfrak g}$. These results constitute a substantial improvement on the structure theory developed in \cite{DOV}. In addition we construct examples of homogeneous Riemannian spaces with non-trivial nullity, where $G$ is a non-solvable group, answering a natural open question. Such examples admit (locally homogeneous) compact quotients. In the case of co-nullity $3$ we give an explicit description of the isometry group of any homogeneouslocally irreducible Riemannian manifold with nullity.
