Generalized Chen's conjecture on biharmonic submanifolds in non-positively curved manifolds

Let MM be a biharmonic submanifold of a non-positively curved Riemannian manifold. Generalized Chen's conjecture. The submanifold MM is minimal. Ou and Tang constructed counterexamples to this conjecture, so the claim is refuted in general. It remains open for biharmonic submanifolds in hyperbolic spaces in the cases described in the source.

Sources & referencesView supporting material

Primary source

Shun Maeta and Miho Shito, “Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature”, arXiv:2509.05939 (2026).

Additional references

7 papers in this index state this conjecture (2007–2025). The statement above is taken from the most recent of them; the others are arXiv:2502.13580, arXiv:2007.13589, arXiv:1308.0420, arXiv:1305.7065, arXiv:1208.0473, arXiv:0705.3961.

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