2 problems

Let $\varphi:M^2\to N^4(\epsilon)$ be a proper biharmonic immersion. Generalized Chen conjecture. Then $\epsilon>0$, so $N^4(\epsilon)$ is the four-dimensional sphere…

Let $\varphi:M^2\to N^4(\epsilon)$ be a non-CMC W-surface with flat normal bundle. Assume that $3f^2+K-\epsilon\neq 0$ and $\nabla^\perp E_3\neq 0$ at any point. Biharmonicity conj…