论文标题
伪里曼尼亚人Sasaki Solvmanifolds
Pseudo-Riemannian Sasaki solvmanifolds
论文作者
论文摘要
We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup $\{\exp tX\}$ is a normal nilpotent subgroup commuting with $\{\exp tX\}$, and $X$ is not浅色。我们以萨萨基（Sasaki）的减少及其伪卡勒（Pseudo-kähler）商的形式来表征这种几何形状，在Reeb Vector Field产生的动作下。 我们将这种类型的伪里曼尼亚人Sasaki Solvmanifolds分类为$ 5 $，而Dimension $ 7 $的Kähler减少的尺寸为$ 7 $。
We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup $\{\exp tX\}$ is a normal nilpotent subgroup commuting with $\{\exp tX\}$, and $X$ is not lightlike. We characterize this geometry in terms of the Sasaki reduction and its pseudo-Kähler quotient under the action generated by the Reeb vector field. We classify pseudo-Riemannian Sasaki solvmanifolds of this type in dimension $5$ and those of dimension $7$ whose Kähler reduction in the above sense is abelian.
