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 ≥ 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.
Polyharmonic surfaces in 3-dimensional homogeneous spaces
Montaldo, Stefano
;Ratto, Andrea
2024-01-01
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 ≥ 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.
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