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arXiv · 2302.06197

Polyharmonic surfaces in $3$-dimensional homogeneous spaces

Stefano Montaldo·Cezar Oniciuc·Andrea Ratto
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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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Stefano Montaldo, Cezar Oniciuc, Andrea Ratto. 2023-02-13. Polyharmonic surfaces in $3$-dimensional homogeneous spaces. https://doi.org/10.1007/s00229-023-01520-4

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