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The classification of ERP G 2 -structures on Lie groups
Annali di Matematica Pura ed Applicata ( IF 1 ) Pub Date : 2020-04-04 , DOI: 10.1007/s10231-020-00977-4
Jorge Lauret , Marina Nicolini

A complete classification of left-invariant closed \(G_2\)-structures on Lie groups which are extremally Ricci pinched (i.e., \( {d}\tau = \tfrac{1}{6}|\tau |^2\varphi + \tfrac{1}{6}*(\tau \wedge \tau )\)), up to equivalence and scaling, is obtained. There are five of them, they are defined on five different completely solvable Lie groups and the \(G_2\)-structure is exact in all cases except one, given by the only example in which the Lie group is unimodular.



中文翻译:

李群上ERP G 2-结构的分类

Lie群上极左Ricci捏住的左不变封闭\(G_2 \)-结构的完整分类(即\({d} \ tau = \ tfrac {1} {6} | \ tau | ^ 2 \ varphi + + tfrac {1} {6} *(\ tau \ wedge \ tau)\)),直到等价和缩放为止。它们有五个,它们在五个不同的完全可解的Lie基团上定义,并且\(G_2 \)-结构在所有情况下都是精确的,只有一个例外,这是唯一的一个例子,其中Lie基团是单模的。

更新日期:2020-04-23
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