r-Harmonic and complex isoparametric functions on the Lie groups Rm⋉Rn and Rm⋉H2n+1
In this paper we introduce the notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper r-harmonic functions. We then apply this to construct the first known explicit proper r-harmonic functions on the Lie group semidirect products Rm⋉ Rn and Rm⋉ H 2n+1, where H 2n+1 denotes the classical (2 n+ 1) -dimensional Hei
