论文标题
关于$ \ mathfrak {g} $ - 歧管的度量结构的RICCI曲率 -
On Ricci curvature of metric structures on $\mathfrak{g}$-manifolds
论文作者
论文摘要
我们研究$ {\ mathfrak {g}} $的RICCI曲率的属性，并特别注意较高维度的Abelian Lie代数案例。研究了特征叶的横向歧管的RICCI曲率与RICCI曲率之间的关系。特别是，在$ {\ mathfrak {g}} $ - 歧管可以是ricci soliton或梯度ricci soliton的情况下，发现了足够的条件。最后，我们在爱因斯坦K-manifolds上获得了一个令人惊奇的（不存在）更高维度的概括，用于特殊的Abelian $ {\ Mathfrak {g}} $ - 流形的特殊类别。
We study the properties of Ricci curvature of ${\mathfrak{g}}$-manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between Ricci curvature of the manifold and the Ricci curvature of the transverse manifold of the characteristic foliation are investigated. In particular, sufficient conditions are found under which the ${\mathfrak{g}}$-manifold can be a Ricci soliton or a gradient Ricci soliton. Finally, we obtain a amazing (non-existence) higher dimensional generalization of the Boyer-Galicki theorem on Einstein K-manifolds for a special class of abelian ${\mathfrak{g}}$-manifolds.
