Biharmonic surfaces of $\mathbb{S}^4$

TL;DR

This paper characterizes proper-biharmonic constant mean curvature surfaces in the 4-sphere as precisely those minimal in a specific 3-sphere, providing a clear geometric classification.

Contribution

It establishes a complete characterization of proper-biharmonic surfaces in , linking them to minimal surfaces in a smaller sphere, which was previously unknown.

Findings

Proper-biharmonic surfaces are minimal in (rac{1}{\u221a2})

Characterization of constant mean curvature surfaces in 

New geometric classification result

Abstract

In this note we prove that a constant mean curvature surface is proper-biharmonic in the unit Euclidean sphere $\mathbb{S}^4$ if and only if it is minimal in a hypersphere $\mathbb{S}^3(\frac{1}{\sqrt{2}})$.