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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… Click to show full abstract
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 .
Journal Title: Journal of Geometry and Physics
Year Published: 2021
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