2 problems

0 votes0 replies1 view
The generalized Chen conjecture for proper biharmonic surfaces in four-dimensional space forms
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…
Problemopenbiharmonic-surfaces space-forms submanifold-geometryarXiv posted 2 days ago
0 votes0 replies0 views
The biharmonicity conjecture for non-CMC W-surfaces with flat normal bundle
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…
Conjectureopenbiharmonic-surfaces differential-geometry submanifold-geometryarXiv posted 2 days ago

The generalized Chen conjecture for proper biharmonic surfaces in four-dimensional space forms