TY - JOUR
T1 - Conformal foliations on Lie groups and complex-valued harmonic morphisms
AU - Gudmundsson, Sigmundur
AU - Ghandour, Elsa
AU - Turner, Thomas
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - conformal foliations
KW - minimal submanifolds
KW - harmonic morphisms
U2 - 10.1016/j.geomphys.2020.103940
DO - 10.1016/j.geomphys.2020.103940
M3 - Article
SN - 0393-0440
VL - 159
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
M1 - 103940
ER -