论文标题
Ricci孤子带有正交不及物的二维Abelian杀死代数
Ricci solitons with an orthogonally intransitive 2-dimensional Abelian Killing algebra
论文作者
论文摘要
在本文中，我们报告了四维Ricci Solitons的本地分类，该分类具有$ 2 $维的Abelian杀死代数$ \ Mathcal {G} _ {2} $，其杀戮叶子是非杀伤和正交的，它的杀戮叶子是无关的。分类是根据以下其他假设获得的：（i）由$ \ Mathcal {g} _ {2} $定义的curvature vector字段，是一个null vector字段； （ii）$ \ MATHCAL {G} _ {2} $具有null vector; （iii）Ricci Soliton的矢量场与杀伤叶和正交分布的对称性相切。由于只有几乎没有正交性的爱因斯坦指标的例子，甚至对正交不及物的RICCI Solitons知之甚少，因此我们认为这些结果可以帮助填补文献中的这一空白。
In this paper we report on a local classification of four dimensional Ricci solitons which have a $2$-dimensional Abelian Killing algebra $\mathcal{G}_{2}$, whose Killing leaves are non-null and orthogonally intransitive. The classification is obtained under the following additional assumptions: (i) the curvature vector field, of the submersion defined by $\mathcal{G}_{2}$, is a null vector field; (ii) $\mathcal{G}_{2}$ has a null vector; (iii) the vector field of the Ricci soliton is tangent to the Killing leaves and a symmetry of the orthogonal distribution. Since there are only few examples of orthogonally intransitive Einstein metrics, and even less is known about orthogonally intransitive Ricci solitons, we believe that these results can help fill this gap in the literature.
