Polyharmonic surfaces in $3$-dimensional homogeneous spaces
Differential Geometry
2025-01-10 v1
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.
Keywords
Cite
@article{arxiv.2302.06197,
title = {Polyharmonic surfaces in $3$-dimensional homogeneous spaces},
author = {Stefano Montaldo and Cezar Oniciuc and Andrea Ratto},
journal= {arXiv preprint arXiv:2302.06197},
year = {2025}
}
Comments
24 pages, 2 figures