BMO conjecture on biharmonic submanifolds in spheres
Let be a biharmonic submanifold of a sphere. BMO conjecture. The submanifold has constant mean curvature. The source presents this as one of the well-known open conjectures in biharmonic submanifold theory, without giving a resolution or specifying additional hypotheses.
References
Primary source
Shun Maeta and Miho Shito, “Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature”, arXiv:2509.05939 (2026).
Additional references
4 papers in this index state this conjecture (2014–2025). The statement above is taken from the most recent of them; the others are arXiv:1801.07879, arXiv:1506.04476, arXiv:1405.5947.
Progress summary
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