A Riemannian submersion from an (n+1)-dimensional constant sectional curvature manifold to an n-dimensional manifold is biharmonic if and only if it is harmonic.
O’Neill,The fundamental equations of a submersion, Michigan Math
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Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature
A Riemannian submersion from an (n+1)-dimensional constant sectional curvature manifold to an n-dimensional manifold is biharmonic if and only if it is harmonic.
- \lambda-biharmonic Riemannian submersions from manifolds with constant sectional curvature