TY - JOUR
T1 - Harmonic morphisms from the classical non-compact semisimple Lie groups
AU - Gudmundsson, Sigmundur
AU - Sakovich, Anna
PY - 2009
Y1 - 2009
N2 - We construct the first known complex-valued harmonic morphisms from the non-compact Lie groups View the MathML source, SU*(2n) and View the MathML source equipped with their standard Riemannian metrics. We then introduce the notion of a bi-eigenfamily and employ this to construct the first known solutions on the non-compact Riemannian SO*(2n), SO(p,q), SU(p,q) and Sp(p,q). Applying a duality principle we then show how to manufacture the first known complex-valued harmonic morphisms from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with semi-Riemannian metrics.
AB - We construct the first known complex-valued harmonic morphisms from the non-compact Lie groups View the MathML source, SU*(2n) and View the MathML source equipped with their standard Riemannian metrics. We then introduce the notion of a bi-eigenfamily and employ this to construct the first known solutions on the non-compact Riemannian SO*(2n), SO(p,q), SU(p,q) and Sp(p,q). Applying a duality principle we then show how to manufacture the first known complex-valued harmonic morphisms from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with semi-Riemannian metrics.
KW - Harmonic morphisms
KW - Minimal submanifolds
KW - Lie groups
U2 - 10.1016/j.difgeo.2008.10.003
DO - 10.1016/j.difgeo.2008.10.003
M3 - Article
SN - 1872-6984
VL - 27
SP - 47
EP - 63
JO - Differential Geometry and its Applications
JF - Differential Geometry and its Applications
IS - 1
ER -