论文标题
纯coclosed g $ _ {\ mathbf2} $ - 2步nilpotent Lie组上的结构
Purely coclosed G$_{\mathbf2}$-structures on 2-step nilpotent Lie groups
论文作者
论文摘要
我们考虑7维2步尼尔氏谎言组上的剩余（纯）coclated g $ _2 $ _2 $ - 结构。根据换向器子组的维度，我们获得了各种标准，这些标准表征了由剩余的纯coclosed g $ _2 $结构引起的riemannian指标。然后，我们使用它们来确定承认这种类型的结构的2步nilpotent Like的同构类别。作为中级步骤，我们表明，在其中一个人中诱发了一个coclated g $ _2 $结构的2步nilpotent lie代数上的每个度量。最后，我们使用结果对2步nilpotent Lie代数的纯cococlosed g $ _2 $结构引起的指标的明确描述，最多具有两个尺寸的代数，最多是两个尺寸的代数。
We consider left-invariant (purely) coclosed G$_2$-structures on 7-dimensional 2-step nilpotent Lie groups. According to the dimension of the commutator subgroup, we obtain various criteria characterizing the Riemannian metrics induced by left-invariant purely coclosed G$_2$-structures. Then, we use them to determine the isomorphism classes of 2-step nilpotent Lie algebras admitting such type of structures. As an intermediate step, we show that every metric on a 2-step nilpotent Lie algebra admitting coclosed G$_2$-structures is induced by one of them. Finally, we use our results to give the explicit description of the metrics induced by purely coclosed G$_2$-structures on 2-step nilpotent Lie algebras with derived algebra of dimension at most two, up to automorphism.
