Conformal foliations on Lie groups and complex-valued harmonic morphisms

Sigmundur Gudmundsson, Elsa Ghandour, Thomas Turner

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number103940
Number of pages11
JournalJournal of Geometry and Physics
Early online date2020 Sept 29
Publication statusPublished - 2021

Subject classification (UKÄ)

  • Geometry


  • conformal foliations
  • minimal submanifolds
  • harmonic morphisms


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