Polyharmonic surfaces in 3-dimensional homogeneous spaces

Abstract

Abstract In the first part of this paper we shall classify proper triharmonic isoparametric surfaces in 3-dimensional homogeneous spaces (Bianchi-Cartan-Vranceanu spaces, shortly BCV-spaces). We shall also prove that triharmonic Hopf cylinders are necessarily CMC. In the last section we shall determine a complete classification of CMC r -harmonic Hopf cylinders in BCV-spaces, $$r \ge 3$$ r ≥ 3 . This result ensures the existence, for suitable values of r , of an ample family of new examples of r -harmonic surfaces in BCV-spaces.