On the existence of harmonic morphisms from certain symmetric spaces

Abstract

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 ∗ ( 2 n ) / Sp ( n ) and their compact duals SU ( n ) / SO ( n ) and SU ( 2 n ) / Sp ( n ) . Furthermore we prove the existence of globally defined, complex-valued harmonic morphisms from any Riemannian symmetric space of type IV.