Proper $r$-harmonic functions from Riemannian manifolds

Abstract

We introduce a new method for constructing complex-valued $r$-harmonic functions on Riemannian manifolds. We then apply this method for the important semisimple Lie groups $SO(n)$, $SU(n)$, $Sp(n)$, $S{L}_n(R)$, $Sp(R,n)$, $SU(p,q)$, $SO(p,q)$, $Sp(p,q)$, $S{O}^{\ast }(2n)$ and $S{U}^{\ast }(2n)$.