Abstract We study left-invariant foliations F on Riemannian Lie groups G generated by a subgroup K . We are interested in such foliations which are conformal and with minimal leaves of codimension two. We classify such foliations F when the subgroup K is one of the important SU ( 2 ) × SU ( 2 ) , SU ( 2 ) × SL 2 ( R ) , SU ( 2 ) × SO ( 2 ) or SL 2 ( R ) × SO ( 2 ) . By this we yield new multi-dimensional families of Lie groups G carrying such foliations in each case. These foliations F produce local complex-valued harmonic morphisms on the corresponding Lie group G .

中文翻译：

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李群上的共形叶理和复值调和态射

摘要 我们研究了由子群 K 生成的黎曼李群 G 上的左不变叶理 F。我们对这样的叶叶很感兴趣，它们是共形的并且具有最小的二维叶。当子群 K 是重要的 SU ( 2 ) × SU ( 2 ) , SU ( 2 ) × SL 2 ( R ) , SU ( 2 ) × SO ( 2 ) 或 SL 2 ( R ) ×SO(2)。通过这种方式，我们产生了在每种情况下都带有这种叶理的李群 G 的新多维族。这些叶理 F 在相应的李群 G 上产生局部复值调和态射。