On the existence of harmonic morphisms from certain symmetric spaces

Details On the existence of harmonic morphisms from certain symmetric spaces On the existence of harmonic morphisms from certain symmetric spaces

2006-03-13

arxiv.org/abs/math/0603297v1

Mathematics

Differential Geometry

18 pages

Scientific paper

10.1016/j.geomphys.2006.03.008

In this paper we give a positive answer to the open existence problem for complex-valued harmonic morphisms from the non-compact irreducible Riemannian symmetric spaces $SL_n(R)/SO(n)$, $SU^*(2n)/Sp(n)$ and their compact duals $SU(n)/SO(n)$ and $SU(2n)/Sp(n)$. Furthermore we prove the existence of globally defined, complex-valued harmonic morphisms from any Riemannian symmetric space of type IV.

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